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AUTHOR: 


FOWLER,  THOMAS,  1832 


TITLE: 


...ELEMENTS  OF 
INDUCTVE  LOGIC 


PLACE: 


OXFORD 


DA  TE : 


1892 


COLUMBIA  UNIVERSITY  LIBRARIES 
PRESERVATION  DEPARTMENT 


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Fowler,  Thomas,  1832- 

...  The  elements  of  inductive  logic  ...  By  Thomas 
Fowler  ...  6th  ed.,  cor.  and  rev.  Oxford,  At  the  Claren- 
don press,  1876.  189r!« 

XXV  ,  lis  365  p.    17^'".     (Clarendon  press  series) 

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Cforcnbon   (pveee  ^ttita 


INDUCTIVE   LOGIC 


FOWLER 


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HENRY   FROWDE 

Oxford  University  Press  Warehouse 

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112  Fourth  Avenue 


Cfarenbon  ^teee  ^mee 


THE    ELEMENTS 


OF 


INDUCTIVE      LOGIC 


DESIGNED  MAINLY 


FOR   THE   USE  OF  STUDENTS  IN  THE   UNIVERSITIES 


BY 


THOMAS    FOWLER,    D.D. 

>  •    • 

Prestdettt  of  Corpus  Christi  College 
And  formerly    Professor    of  Logic    in    the    University    of  Oxford 
Honorary   Doctor   of  Laws    in    the    University  of  Edinburgh 


SIXTH    EDITION,    CORRECTED    AND    REVISED 


AT    THE    CLARENDON     PRESS 


M  DCCC  XCII 


OxforJ> 

PKINTF.D    AT    THK    (    UARKNPON     PKKSS 
W   ItORACK    HART,   PRINTF.K   TO  THE  VNIVERSITY 


6 


PREFACE  TO  THE  FIRST  EDITION 


-♦♦ 


The  object  of  the  following  work  is  to  serve  as  an 
introduction  to  that  branch  of  scientific  method  which 
is  known  as  Induction.  It  is  designed  mainly  for  the 
use  of  those  who  have  not  time  or  opportunity  to  con- 
sult larger  works,  or  who  require  some  preliminary 
knowledge  before  they  can  profitably  enter  upon  the 
study  of  them. 

To  the  works  of  Mr.  Mill,  Dr.  Whewell,  and  Sir  John 
Herschel,  the  Author  must,  once  for  all,  express  his  obli- 
gations. '  He  has,  however,'  if  he  may  be  allowed  to 
repeat  the  language  already  employed  in  the  Preface 
to  his  Manual  of  Deductive  Logic,  *  endeavoured,  on  all 
disputed  points,  to  reason  out  his  own  conclusions,  feel- 
ing assured  that  no  manual,  however  elementary,  caVi  be 
of  real  service  to  the  student,  unless  it  express  what  may 
be  called  the  "  reasoned  opinions  "  of  its  author.' 

The  analysis  of  Induction  presents  far  more  difficulties 
than  that  of  Deduction,  and  requires  to  be  illustrated 
by  far  more  numerous  and  intricate  examples.  But, 
on  the  other  hand,  it  is  more  interesting  both  to  the 

350582 


VI 


PREFACE    TO    THE   FIRST  EDFTION. 


teacher  and  to  the  student ;  and,  being  a  comparatively 
recent  study,  is  less  hampered  by  conventionalities  of 
treatment.  Since  the  time  of  Bacon,  it  has  always,  with 
more  or  less  of  success,  claimed  a  place  in  liberal 
education,  and  many,  to  whom  the  technical  terms  and 
subtle  distinctions  of  the  older  logic  are  justly  repulsive, 
have  experienced  a  peculiar  delight  in  attempting  to 
discover  and  test  the  grounds  on  which  the  results  of 
modern  science  mainly  rest. 

The  study  of  Deductive  Logic  can  be  of  little  service 
unless  it  be  supplemented  by,  at  least,  some  knowledge 
of  the  principles  of  Induction,  which  supplies  its  pre- 
misses. Many  of  the  objections  directed  against  the 
study  of  Logic  are  due  to  the  narrow  conceptions  which 
are  entertained  of  its  province,  and  might  be  easily  met 
by  showing  that  the  study,  when  we  include  both  its 
parts,  has  a  much  wider  range  than  is  popularly  assigned 

to  it. 

Though  the  present  work  is  mainly  intended  for  stu- 
dents in  the  Universities,  it  is  hoped  that  it  will  be  found 
to  pfesent  some  interest  for  the  general  reader,  and  that 
it  may  be  useful  to  students  of  medicine  and  the  physical 
sciences,  as  well  as  to  some  of  the  more  advanced 
scholars  in  our  Public  Schools. 

The  number  of  scientific  examples  adduced  throughout 
the  work  renders  it  necessary,  perhaps,  that  the  Author 
should  state  emphatically  that  the  work  is  intended  as  an 


PREFACE    TO    THE  FIRST  EDITION, 


vu 


introduction,  not  to  science,  but  to  scientific  method.  Its 
object  is  not  to  give  a  resume  of  the  sciences,  physical 
or  social,  a  task  for  which  the  Author  would  be  wholly 
incompetent,  but  to  show  the  grounds  on  which  our 
scientific  knowledge  rests,  the  methods  by  which  it  has 
been  built  up,  and  the  defects  from  which  it  must  be 
free.  Notwithstanding  its  frequent  incursions  into  the 
domain  of  science,  the  purport  of  the  work  must  be 
regarded  as  strictly  logical. 

The  examples  have,  as  a  rule,  been  selected  from  the 
physical  rather  than  the  social  sciences,  as  being  usually 
less  open  to  dispute,  and  lying  within  a  smaller  compass. 
Wherever  it  has  been  possible,  they  have  been  given  in 
the  exact  words  of  the  author  from  whom  they  are  taken. 

Some  of  the  more  complicated  cases  of  inductive 
reasoning,  such  as  those  which  deal  with  Progressive 
Causes  or  Intermixture  of  Effects,  have,  if  alluded  to 
at  all,  been  only  briefly  noticed.  Any  detailed  examina- 
tion of  these  more  intricate  questions  seemed  to  lie 
without  the  scope  of  the  treatise.  The  student  who  has 
leisure  to  pursue  the  subject  will  find  ample  information 
in  the  pages  of  Mr.  Mill's  Logic. 

It  only  remains  for  the  Author  to  express  his  grateful 
acknowledgments  to  those  who  have  assisted  him  in  the 
execution  of  the  work.  These  are,  in  the  first  place,  due 
to  Dr.  Liddell,  Dean  of  Christ  Church,  through  whose 
hands  the  sheets  have  passed,  and  who,  in  addition  to 


Vlll 


PREFACE    TO    THE  FIRST  EDITION, 


revising  the  proofs,  has,  from  time  to  time,  offered  many 
very  valuable  suggestions.  They  are  due  also,  in  no 
small  degree,  to  Sir  John  Herschel  and  Professor  Bar- 
tholomew Price,  who  most  kindly  undertook  to  revise 
the  scientific  examples;  to  Professors  Rolleston  and 
Clifton,  who  have  frequently  allowed  the  Author  to  con- 
sult them  on  questions  connected  with  the  subjects  of 
their  respective  chairs,  and  to  the  Rev.  G.  W.  Kitchin, 
the  Organising  Secretary  of  the  Clarendon  Press  Series. 
The  Author  must,  however,  be  regarded  as  alone  re- 
sponsible for  any  errors  which  may  occur  either  in  the 
theoretical  portion  of  the  work  or  in  the  examples. 

Lincoln  College, 
Oct.  30,  i86y. 


PREFACE  TO  THE  THIRD  EDITION 


-M- 


[The  student  is  requested  to  read  this  Preface  in 
connexion  with  Chapter  III.] 


-♦♦- 


Since  the  publication  of  my  second  Edition,  there  has 
appeared  an  important  work  on  Scientific  Method,  entitled 
*  The  Principles  of  Science,'  by  Professor  Stanley  Jevons, 
of  Owens  College,  Manchester.  To  this  book  I  have 
made  occasional  references  in  the  foot-notes  to  my  present 
edition.  But,  as  I  differ  entirely  from  Professor  Jevons 
on  the  fundamental  (question  of  the  validity  of  our  induc- 
tive inferences,  I  think  it  desirable  to  offer  a  few  remarks 
on  this  point  in  the  present  place,  rather  than  to  intro- 
duce controversial  matter  into  the  body  of  the  work. 

Mr.  Jevons  over  and  over  again  asserts  the  uncertainty, 
or  the  mere  probability,  of  all  inductive  inferences.  Thus, 
for  instance,  in  his  chapter  on  the  Philosophy  of  Induc- 
tive Inference,  he  says : — '  I  have  no  objection  to  use 
the  words  cause  and  causation,  provided  they  are  never 
allowed  to  lead  us  to  imagine  that  our  knowledge  of 
nature  can  attain  to  certainty \'  And  again:  *We  can 
never  recur  too  often  to  the  truth  that  our  knowledge  of 

^  Vol.  i.  p.  260. 


X  PREFACE   TO   THE   THIRD   EDITION. 

the  laws  and  future  events  of  the  external  world  is  only 
probablel'  Once  more:  'By  induction  we  gain  no 
certain  knowledge ;  but  by  observation,  and  the  inverse 
use  of  deductive  reasoning,  we  estimate  the  probability 
that  an  event  which  has  occurred  was  preceded  by  con- 
ditions of  specified  character,  or  that  such  conditions 
will  be  followed  by  the  event'.' 

At  the  same  time,  I  am  quite  unable  to  reconcile  with 
these  passages  other  passages,  such  as  those  in  which 
Mr.  Jevons  says:  *We  know  that  a  penny  thrown  into 
the  air  will  certainly  fall  upon  a  flat  side,  so  that  either 
the  head  or  tail  will  be  uppermost','  or,  '  I  can  be  certain 
that  nitric  acid  will  not  dissolve  gold,  provided  I  know 
that  the  substances  employed  really  correspond  to  those 
on  which  I  tried  the  experiment  previously".' 

But,  waiving  the  question  of  inconsistency,  I  maintain 
as  against  Mr.  Jevons  that  many  of  our  inductive  infer- 
ences have  all  the  certainty  of  which  human  knowledge 
is  capable.  Is  the  law  of  gravitation  one  whit  less  certain 
than  the  conclusion  of  the  47th  Proposition  of  the  First 
Book  of  Euclid?  Or  is  the  proposition  that  animal  and 
vegetable  life  cannot  exist  without  moisture  one  whit  less 
certain  than  the  truths  of  the  multiplication  table  ?  Both 
these    physical   generalisations   are    established    by   the 

»  Vol.  i.  p.  271.  '  Ifl.  P-  257- 

♦  Id.  p.  228.     Mr.  Jevons,  however,  curiously  enough  is  not  cer- 
tain about  the  truth  of  the  Law  of  Gravitation.     See  below. 
^  Id.  p.  270. 


CERTAINTY  OF  INDUCTIVE  REASONING.      XI 


Method  of  Difference,  and,  as  actual  Laws  of  Nature, 
admit,  I  conceive,  of  no  doubt.  But  it  may  be  asked 
if  they  will  always  continue  to  be  Laws  of  Nature? 
I  reply  that,  unless  the  constitution  of  the  Universe  shall 
be  changed  to  an  extent  which  I  cannot  now  even  con- 
ceive, they  will  so  continue,  and  that  no  reasonable  man 
has  any  practical  doubt  as  to  their  continuance.  And 
why?  Because  they  are  confirmed  by  the  whole  of  our 
own  experiences,  which  in  both  these  cases  is  of  enormous 
extent  and  variety,  by  the  experience  of  our  ancestors, 
and  by  all  that  we  can  ascertain  of  the  past  history  of 
nature,  while  their  reversal  would  involve  the  reversal  of 
almost  all  the  other  laws  with  which  we  are  acquainted. 
Still,  it  must  be  confessed  that  all  our  inferences  from 
the  present  to  the  future  are,  in  one  sense,  hypothetical, 
the  hypothesis  being  that  the  circumstances  on  which 
the  laws  themselves  depend  will  continue  to  be  the  same 
as  now,  that  is,  in  the  present  case,  that  the  constitution 
of  nature,  in  its  most  general  features,  will  remain  un- 
changed ;  or,  to  put  it  in  still  another  form,  that  the  same 
causes  will  continue  to  produce  the  same  effects.  What 
would  happen  if  this  expectation  were  ever  frustrated,  it 
is  absolutely  impossible  for  us  to  say,  so  completely  is  it 
assumed  in  all  our  plans  and  reasonings. 

We  may  say,  then,  that  there  are  many  inductions  as 
to  the  actual  constitution  of  nature  which  we  may  accept 
with  certainty,  while,  with  respect  even  to  the  distant 


xii  PREFACE   TO   THE    THIRD   EDITION, 

future,  we  may  accept  them  with  equal  certainty,  on  the 
hypothesis  that  the  general  course  of  nature  will  not  be 
radically  changed.  And  if  the  general  course  of  nature 
were  changed,  might  not  the  change  affect  our  faculties 
as  well  as  the  objects  of  our  knowledge;  and,  in  that 
case,  are  we  certain  that  we  should  still  regard  things 
that  are  equal  to  the  same  thing  as  equal  to  one  another, 
or  assume  that  a  thing  cannot  both  be  and  not  be  in  the 
same  place  at  the  same  time  ?  There  is,  in  fact,  no  limit 
to  the  possibility  of  scepticism  with  regard  to  the  per- 
sistency either  of  the  laws  of  external  nature  or  of  the 
laws  of  mind.  But  all  our  reasonings  depend  on  the 
hypothesis  that  the  most  general  laws  of  matter  and  the 
most  general  laws  of  mind  will  continue  to  be  what  they 
are,  and  of  the  truth  of  this  hypothesis  no  reasonable 
man  entertains  any  practical  doubt ^ 

There  is,  then,  I  contend,  no  special  uncertainty 
attaching  to  the  truths  arrived  at  by  induction.  They 
are,  indeed,  like  all  other  truths,  relative  to  the  present 
constitution  of  nature  and  the  present  constitution  of 
the  human  mind,  but  this  is  a  limitation  to  which  all 
our  knowledge  alike  is  subject,  and  which  it  is  vain  for 
us  to  attempt  to  transcend.  Syllogistic  reasoning  implies 
a  particular  constitution  of  the  mind,  as  much  as  induc- 

•  Thus  Mr.  Jevons,  who,  when  he  begins  to  theorise,  has  doubts  as 
to  the  truth  of  the  Law  of  Gravitation,  has  no  doubt,  when  he  throws 
a  penny  up  into  the  air,  that  it  will  fall  on  a  flat  side. 


jevons"  theory  of  induction,  xiii 

live  reasoning  implies  a  particular  constitution  of  nature. 
Both  mind  and  nature  might,  of  course,  be  radically 
changed  by  an  omnipotent  power,  but  what  the  con- 
sequences of  that  change  might  be  it  is  utterly  impossible 
for  us  to  say. 

The  uniformity  of  nature,  the  trustworthiness  of  our 
own  faculties— these  are  the  ultimate  generalisations 
which  lie  at  the  root  of  all  our  beliefs,  and  are  the  con- 
ditions of  all  our  reasonings.  It  is,  of  course,  always 
possible  to  insinuate  doubts  as  to  either,  but,  however 
curious  and  entertaining  such  doubts  may  be,  they  have 
no  practical  influence  even  on  those  who  originate  them. 
Even  Mr.  Jevons  himself,  we  have  seen,  when  not  under 
the  dominion  of  his  theory,  speaks  of  some  of  the 
results  of  induction  as  certain,  and  we  can  hardly 
conceive  men  of  science  commonly  speaking  of  the  most 
firmly  established  generalisations  of  mechanics,  optics, 
or  chemistry,  simply  as  conclusions  possessing  a  high 
degree  of  probability. 

Still,  Mr.  Jevons,  appearing  not  in  the  character  of 
a  physicist,  but  of  a  logician,  tells  us  that  '  the  law  of 
gravitation  itself  is  only  probably  true^'  It  would  be 
interesting  to  learn  what  is  the  exact  amount  of  this 
'probability,'  or,  if  it  be  meant  that  we  can  only  be 
certain  that  the  force  of  gravity  is  acting  here  and  now, 
it  would  be  an  interesting  enquiry  to  ascertain  what  is 

^  p.  zoo. 


xiv         PREFACE   TO   THE   THIRD   EDITION. 

the  exact  value  of  the  'probability'  that  it  is  at  this 
moment  acting  in  Manchester  as  well  as  in  Oxford,  or 
that  it  will  be  acting  at  this  time  to-morrow  as  well  as 

to-day. 

But,  if  the  conclusions  of  Induction  are  thus  uncertain, 

where,  according  to  Mr.  Jevons,  are  we  to  find  certainty  ? 
'  Certainty  belongs  only  to  the  deductive  process  and  to 
the  teachings  of  direct  intuition^'     Does  it  then  belong 
to  the  conclusions  of  deduction  ?     Apparently  not,  for, 
at  the  very  beginning  of  the  wo^k^  we  are  told  that 
'  in  its  ultimate  origin  or  foundation,  all   knowledge   is 
inductive,'  and  Mr.  Jevons  is,  of  course,  too  practised  a 
logician  to  suppose  that  the  conclusion  can  be  more 
certain  than  the   premisses.     The   conclusions  of  geo- 
metry, therefore,  partake  of  the  same  '  uncertainty '  as  the 
results    of  the    physical    sciences,    and    the    region    of 
'  certainty '  is  confined  to  our  direct  intuitions  and  to  the 
rules  of  syllogism  (supposing,  that  is,  a  difference  to  be 
intended  between  the  '  deductive  process '  and  deductive 
results).     I  venture  to  suggest  that  this  small  residuum 
of  '  certainty '  would  soon  yield  to  solvents  as  powerful  as 
those  which  Mr.  Jevons  has  applied   to   the  results  of 
induction  (and  apparently  also  of  deduction)  ;  and  that, 
therefore,  its  inherent  '  uncertainty '  is  no  special  charac- 
teristic of  that  method,  but  one  which  it  shares  with  all 
our  so-called  knowledge. 


p-  309- 


p.  14. 


ALL  REASONING  HYPOTHETICAL, 


XV 


The  fact  is  that  in  all  reasoning,  whether  inductive  or 
deductive,  we  make,  and  must  make,  assumptions  which 
may  theoretically  be  questioned,  but  of  the  truth  of 
which  no  man,  in  practice,  entertains  the  slightest  doubt. 
Thus,  in  syllogistic  reasoning,  we  assume  at  every  step 
the  trustworthiness  of  memory ;  we  assume,  moreover, 
the  validity  of  the  premisses,  which,  as  Mr.  Jevons 
acknowledges,  must  ultimately  be  guaranteed  either  by 
induction  or  direct  observation ;  lastly,  we  assume  the 
validity  of  the  primary  axioms  of  reasoning,  which,  ac- 
cording to  different  theories,  are  either  obtained  by 
induction  or  assumed  to  be  necessary  laws  of  the 
human  mind.  In  this  sense,  all  reasoning  and  all 
science  is  hypothetical,  and  the  assumption  of  the  Uni- 
formity of  Nature  does  not  render  inductive  reasoning 
hypothetical  in  any  special  sense  of  the  term.  For,  if 
the  Laws  of  the  Uniformity  of  Nature  and  of  Universal 
Causation  admit  of  exceptions  or  are  liable  to  ultimate 
frustration,  so,  for  aught  we  know,  may  the  axioms  of 
syllogistic  reasoning  or  the  inductions  by  which  we  have 
established  the  trustworthiness  of  our  faculties.  And, 
if  the  conceptions  of  uniformity  and  causation  be  purely 
relative  to  man,  so,  for  aught  we  know,  may  be  the 
so-called    laws    of    thought    themselves^".     Induction 

*"  According  to  the  view  of  the  nature  and  ultimate  origin  of 
human  knowledge,  accepted  both  by  Mr.  Jevons  and  myself,  it  is, 
in  fact,  no  paradox  but  a  mere  truism  to  say  that  the  fundamental 
axioms  of  reasoning  are  themselves  only  particular  uniformities  of 


XVI 


PREFACE    TO    THE   THIRD  EDITION, 


would  only  be  hypothetical  in  a  special  sense,  if  we 
had  any  reasonable  ground  for  doubting  the  truth  of 
the  hypotheses^'  on  which  it  rests. 

But  as,  *in  its  ultimate  origin  or  foundation,  all 
knowledge'  (including,  of  course,  that  of  the  laws 
which  govern  the  syllogistic  process  itself)  'is  induc- 
tive,' Professor  Jevons  must  either  employ  the  word 
'  certain '  in  a  variety  of  senses,  or  he  must  be  prepared 
with  the  philosophers  of  the  New  Academy  to  maintain 
the  uncertainty  of  all  knowledge  whatsoever. 

Such,  as  it  appears  to  me,  are  the  inconsistencies 
and  paradoxes  into  which  a  very  able  writer  has  been 
led  by  a  tendency  to  over-refinement,  and,  still  more 
perhaps,  by  a  desire  to  apply  the  ideas  and  formulae  of 
mathematics  to  the  explanation  of  logical  problems. 

I  must  further  express  my  dissidence  from  Mr.  Jevons' 
statement  that  all  inductive  inference  is  preceded   by 

nature,  arrived  at  by  the  same  evidence  and  depending  for  their 
justification  on  the  same  grounds  as  those  ultimate  generalisations 
on  causation  to  which  we  give  the  special  names  of  the  Law  of 
Universal  Causation  and  the  Law  of  the  Uniformity  of  Nature. 

"  I  need  hardly  say  that  I  am  not  here  using  the  word  '  hypothesis ' 
in  the  sense  of  an  unverified  assumption.  Reasoning,  both  in- 
ductive and  deductive,  is  found  on  analysis  to  depend,  in  the  last 
resort,  on  certain  assumptions  or  hypotheses,  but  then  the  truth 
of  these  assumptions  or  hypotheses  is  guaranteed  by  the  whole 
experience  of  the  human  race,  past  and  present,  and  beyond  this 
guarantee  I  conceive  that  there  is  no  other  attainable.  In  other 
words,  all  truth  is  relative  to  our  faculties  of  knowing,  and  this 
condition  it  is  in  vain  for  us  to  attempt  to  transcend. 


/ 


jevons'  theory  of  induction.  xvii 

hypotheses'^,  from  his  theory  that  Induction  is  simply 
the  Inverse  Method  of  Deduction,  and,  above  all,  from 
what  appears  to  me  to  be  the  exceedingly  misleading 
parallel  drawn  between  Nature  and  a  ballot  -  box. 
*  Events,'  says  Mr.  Jevons,  '  come  out  like  balls  from 
the  vast  ballot-box  of  Nature".'  Now  the  balls  were 
placed  in  the  ballot-box  by  human  hands ;  the  number 
and  character  of  them  may  have  been  due  merely  to 
caprice  or  chance;  moreover,  they  are  all  isolated 
entities  having  no  connexion  with  each  other.  Would 
it  be  possible  to  find  a  stronger  contrast  to  the  works 
of  Nature?  If  natural  phenomena  did  indeed  admit 
only  of  the  same  kind  of  study  as  the  drawing  of  balls 
from  a  ballot-box,  Mr.  Jevons'  conception  of  Induction 
would  undoubtedly  be  the  true  one,  and  I  should 
agree  with  him  that  *  no  finite  number  of  particular 
verifications  of  a  supposed  law  will  render  that  law 
certain.'  But,  ju.st  because  we  believe  that  the  opera- 
tions of  Nature  are  conducted  with  an  uniformity  for 
which  we  seek  in  vain  amongst  the  contrivances  of 
men,  do  we  regard  ourselves  as  capable,  in  many  cases, 
of  predicting  the  one  class  of  events  with  certainty, 
while  the  other  affords  only  matter  for  more  or  less 
probable  conjecture. 

Intimately  connected  with  Mr.  Jevons'  depreciation  of 
the  value  of  the  inductive  inference  is  his  statement  that 


'^  See  chap.  i.  pp.  11-13,  of  this  work. 

b 


^^  Vol.  i.  p.  275. 


xviii       PREFACE   TO    THE    THIRD  EDITION. 

Induction  is  simply  the  inverse  method  of  Deduction. 
If    Induction    simply   consists    in    framing   hypotheses, 
deducing  consequences  from  the  hypotheses,  and  then 
comparing  these  consequences  with  individual  facts  for 
the  purpose  of  verifying  them  by  specific  experience  ^\ 
I  grant   that   the   procedure   must,   in   most  cases,   be 
very  untrustworthy.     In  my  first  Appended  Note  to  my 
Section  on  Hypothesis,  I  have  examined  this  account 
of  Induction,  which   is  virtually  identical  with  that  of 
Dr.  Whewell.      In    opposition    to    it,    I    maintain    the 
following  theses,  which  are  explained  and  defended  in 
the  course  of  my  work:     i.    That  our  inductions  are 
not  always  preceded  by  hypotheses  (and  it  might  be 
added  that,  even  where  they  are,  the  hypothesis  itself 
must  rest  originally  on  some  basis  of  fact,   that   is  to 
say,  on  some  induction  or  other,  however   imperfect; 
for  a  hypothesis  must  always   be   suggested  by  some- 
thing of  which  we  have  had  experience) ;    2.  That  the 
mere  verification  of  our  hypotheses  by  specific  experi- 
ence is  not  sufficient  to  constitute  a  valid   induction, 
unless  the  instances  conform  with  the  requirements  of 
one  of  the  inductive  methods,  or  (as  in  the  case  of  the 
fundamental  laws  of  inductive  reasoning)  be  coextensive 
with  the  whole  experience  of  mankind.     Induction,  I 
maintain,  may  or  may  not  employ  hypothesis,  but  what 
is  essential  to  it  is  the  inference  from  the   particular 

'♦  Vol.  i.  pp.  307,  308. 


ASSUMPTIONS  OF  REASONING. 


XIX 


to  the  general,  from  the  known  to  the  unknown,  and 
the  nature  of  this  inference  it  is  impossible  to  re- 
present adequately  by  reference  to  the  forms  of 
deduction  ^\ 


15 


^  For  the  word  *  adequately,'  I  ought  to  substitute  the  expression, 
'  without  a  considerable  amount  of  circumlocution/  as  the  essential 
difference  between  inductive  and  deductive  reasoning  consists,  not  so 
much  in  the  form  of  the  argument,  as  in  the  nature  of  the  assump- 
tions made:  scientific  induction  postulating,  in  addition  to  the 
assumptions  made  in  deductive  reasoning,  the  laws  of  Universal 
Causation  and  of  Uniformity  of  Nature,  in  its  strictest  sense  (see 
p.  9,  note  7);  and  Inductio  per  Enumerationem  Simplicem,  the 
latter  law  in  its  vaguer  sense.  I  think  it  may  be  useful  to  the 
student  here  to  transcribe  a  note  which  first  appeared  in  the  9th, 
and  is  now  repeated,  with  some  modifications,  in  the  loth  edition 
of  my  Deductive  Logic  (p.  75,  note  3). 

*  If  we  state  explicitly  all  the  assumptions  made  in  the  inductive 
process,  the  conclusion  is  contained  in  the  premisses,  and  the  form  of 
the  reasoning  becomes  deductive  ;  but  it  is  seldom  that  we  do  state 
our  assumptions  thus  explicitly.  The  most  essential  distinction, 
however,  between  inductive  and  deductive  reasoning  consists  not  in 
the  form  of  the  inferences,  but  in  the  nature  of  the  assumptions  on 
which  they  rest.  Deductive  reasoning  rests  on  certain  assumptions 
with  regard  to  language  and  co-existence  (namely,  the  Law  of  Con- 
tradiction, the  Law  of  Excluded  Middle,  and  the  Canons  of  Syl- 
logism), while  inductive  reasoning  assumes  over  and  besides  these 
laws  the  truth  of  the  Laws  of  Universal  Causation,  of  the  Uniformity 
of  Nature  and,  as  implied  in  the  latter,  of  the  Conservation  of 
Energy  ;  or,  if  it  be  of  the  unscientific  description  which  is  known  as 
Inductio  per  Enumerationem  Simplicem,  it  merely  assumes,  instead 
of  them,  the  vague  and  wide  principle  that  the  unknown  resembles, 
or  will  resemble,  the  known.  It  hardly  needs  to  be  added  that 
all  reasoning  alike  assumes  the  trustworthiness  of  present  con- 
sciousness and  of  memory. 

Amongst  the  assumptions  or  pre-suppositions  of  reasoning,  I  have 
not  included  the  so-called  Law  of  Identity ;  as  to  say  that  all  A  is  A, 

b2 


XX 


PREFACE    TO    THE    THIRD   EDITION, 


Mr.  Jevons'  statement  that  'induction  is  really  the 
reverse  process  of  deduction'  I  am  wholly  unable  to 
reconcile  with  the  following  statements  which  occur 
in  the  very  same  page^'':  'In  its  ultimate  origin  or 
foundation  all  knowledge  is  inductive,'  and  'only  when 
we  possess  such  knowledge,  in  the  form  of  general 
[)ropositions  and  natural  laws,  can  we  usefully  apply 
the  reverse  process  of  deduction  to  ascertain  the  exact 
information  required  at  any  moment.'  When  we  com- 
pare these  statements,  the  circle  seems  complete.  A 
precedes  B,  and  B  precedes  A.  A  depends  for  its 
validity  on  B,  and  B  depends  for  its  validity  on  A. 
No  wonder  that  human  reasoning  affords  us  no 
'certain'  results. 

In  offering  these  criticisms  on  some  fundamental 
points  of  difference  between  Mr.  Jevons  and  myself, 
I  am  far  from  denying  the  utility  of  many  portions 
of  his  work,  especially  the  chapters  on  the  Methods 
of  Measurement  and  on  Hypothesis. 

In  the  present  Edition  of  this  work,  I  have  occa- 
sionally   availed   myself  of   the    '  Inductive    Logic '   of 

or  a  thing  is  the  same  as  itself,  appears  to  me  to  be  an  utterly  un- 
meaning proposition.  Mr.  Mill  (Examination  of  Hamilton,  ch.  21), 
in  attempting  to  give  a  meaning  to  this  maxim,  really  transforms 
it  into  a  perfectly  distinct  j>roposition,  namely,  that  Language  may 
express  the  same  idea  in  different  forms  of  words.' 
'•*  Vol.  i.  p.  14. 


PREFACE   TO    THE  FIFTH  EDITION.         XX i 

Mr.  Bain,  a  work  which,  though  it  does  not,  in  my 
opinion,  supersede  Mr.  Mill's  Logic,  supplies  on  some 
points  a  valuable  complement  to  it. 

In  this,  as  in  the  last  Edition,  I  have  to  acknowledge 
the  kindness  of  Professor  Park  of  Belfast,  whose  cor- 
rections and  suggestions  have  enabled  me  to  make 
both  my  works  more  accurate  and  serviceable  than 
they  would  otherwise  have  been. 

Lincoln  College, 
Feb.  24,  1876. 


*^*  In  the  third  Edition  some  new  matter  was  in- 
troduced, bearing  mainly  on  the  following  subjects  : 
Uniformities  of  Coexistence,  the  Historical  Method, 
the  distinction  between  Inductio  per  Enumerationem 
Simplicem  and  the  Method  of  Agreement,  the  constant 
alternation  in  practice  of  the  inductive  and  deductive 
processes,  and  the  Argument  from  Universal  Consent. 
In  the  fourth  Edition  the  principal  alterations  were  the 
introduction  of  new  foot-notes  on  the  definition  of 
Induction  and  on  the  Plurality  of  Causes,  and  some 
additional  remarks  on  the  nature  of  the  Method  of 
Residues  and  on  Empirical  Laws. 

In  the  fifth  Edition,  the  alterations  were  more  nu- 
merous than  in  either  of  the  two  preceding  editions. 
Through  the  kindness  of  my  friend,  Mr.  George  Griffith 

b3 


xxii        PREFACE   TO   THE  SIXTH  EDITION, 

of  Harrow,  I  was  enabled  to  state  some  of  the  scientific 
examples  in  a  more  precise  form  than  in  the  preceding 
editions,  notably  those  on  Double-Weighing  (p.  47),  on 
the  '  Red  Flames '  seen  during  a  total  eclipse  of  the 
Sun  (pp.  50-1),  and  on  Spectrum  Analysis  as  applied  to 
the  constitution  of  the  Sun  and  other  heavenly  bodies 
(pp.  165-7).  The  principal  alterations  or  additions  in 
the  logical  matter  were  on  pp.  204-5  (the  Historical 
Method),  p.  206  (the  Comparative  Method),  pp.  277-8 
(the  Fallacy  of  '  Exaggerated  Comparison '),  and  the 
addition  of  an  important  foot-note  (note  15,  p.  xix)  to 
the  '  Preface  to  the  Third  TMition,'  on  the  peculiar 
nature  of  Inductive  Reasoning  and  on  the  assumptions 
made  in  it.  The  following  foot-notes  were  either  new 
or  contained  additional  matter  :  n.  4,  p.  6  ;  n.  11,  p.  13  ; 
n.  22,  p.  23;  n.  41,  pp.  107-8;  n.  5,  p.  129;  n.  27, 
p.  166  ;  n.  44,  p.  191  ;  n.  54,  P-  205  ;  n.  55,  pp.  205-7  ; 
n.  63,  p.  214  ;  n.  24,  pp.  281-2  ;  n.  26,  p.  282  ;  n.  29, 
p.  283  ;  n.  80,  p.  343. 

liesides  a  few  corrections  in  some  of  the  scientific 
examples,  oc(  asioncd  by  recent  discoveries,  the  principal 
difference  between  this  (the  sixth)  and  former  editions  is 
the  addition  and  alteration  of  certain  passages  in  the 
notes  on  the  Argument  from  Final  Causes,  pp.  342-4- 

c.  c.  c. 

Aug.  18,  1892. 


CONTENTS 


-♦4- 


i:hap. 


I.  The  Nature  of  Inductive  Inference  . 

II.   I 'recesses  subsidiary  to  Induction    . 

§   I .  Observation  and  Experiment 


§   2,  Classification,  Nome 
(i)  Classification 

(2)  Nomenclature 

(3)  Terminology 
§  3.  Hypothesis 

III.  The  Inductive  Methods    . 
Method  of  Agreement 
Method  of  Difi^erence 
Double  Method  of  Agreement 
Method  of  Residues  . 
Method   of  Concomitant  \'ariations 
Historical  Method)    . 

1\'.   Imperfect  Inductions 

Inductio  per  Enumerationcm  Simpl 
Argument  from  Analogy  . 
Imperfect  applications  of  the  Induct 
Incomplete  Inductions) 


iclature,  and  Terminology 


including   the 


icem 


ive  Methods    or 


f  AGE 

3 

39 
39 

5-' 
52 

92 

97 

124 
130 
14S 
160 
173 

i<^3 

219 
219 
226 


•  -^37 


XXIV 


CHAP. 


CONTENTS. 


I'ACE 

V.  The  Relation  of  Induction  to  Deduction,  and  Verification     241 

VI.  The  Fallacies  incident  to  Induction  ....     254 

A.  Fallacies  incident  to  the  subsidiary  processes  .         .254 

I.  Fallacy  of  Non-observation,  consisting  in  neglect  either 

(i)  of  some   of  the  instances  (including  Fallacy 
arising   from   the  confusion   between    Ab- 
solute and  Relative  Frequency)  . 
or  (2)  of  some  of  the  circumstances  attendant  on  a 
given  instance     ...... 

II.  Fallacy   of  Mal-observation   (including   Fallacy  of 

Exaggerated  Comparison) 

III.  Errors  incidental  to  the  operations  of  Classification, 

Nomenclature,  Terminology,  and  Hypothesis 

B.  Fallacies  incident  to  the  Inductive  process  itself,  or  Falla- 
cies of  Generalisation 

IV.  Error  originating  in  the  employment  of  the  Inductio 

per  Enumerationem  Simplicem  (including  the  ille- 
gitimate use  of  the  Argument  from  Authority  and 
of  that  from  Universal  Consent)  .... 
\ .  I'.rrors  common  to  the  employment  of  the  various  In- 
ductive Methods 

(^1)  Mistaking  a  for  the  cause  of/;,  when  the  real 
cause  is  c  (of  which  one  instance  is  neglecting 
to  take  account  of  the  Plurality  of  Causes)    . 
(2)  Mistaking  a  for  the  sole  cause,  when  a  and  r 
are  the  joint  causes,  either  as 
(a)  both  contributing  to  the  total  effect 
or  (j8)  being  both  essential  to  the  production  of 
any  effect  whatever       .         .         .         .         • 
'3)  Mistaking  joint  effects  for  cause  and  effect 


254 
268 

272 

278 

279 


280 


29S 


300 

306 

309 
3H 


CONTENTS, 


XXV 


CHAP. 


(4)  Mistaking  the  remote  cause  for  the  proximate 

cause,  or  the  reverse     .         .         .         .         • 

(5)  Neglecting  to  take  into  account  the  mutual 

action  (mutuality)  of  cause  and  effect   . 

(6)  Inversion  of  cause  and  effect    .... 

VI.  False  analogy  (including  the  illegitimate  use  of  the 
Argument  from  Antiquity,  and  of  the  Argu- 
ment from  Final  Causes)      .... 


PACK 

322 
325 


Index 


329 
357 


*Ek  irpoyivaxTKoyLivaiV  bi  rraaa  SiSaaKoXia,  aairep  kol  iv  Tois 
dvaXvTiKols  Xeyofifv'  r]  fxev  yap  bC  enayay^s,  r]  Be  (rvWoyia-fia. 
'H  fxh  br]  inayayrj  npxh  ^^^^^  f"'*  ''oi'  Ka66\ov^  6  bk  avWoyiCTfios 
€K  Ta)V  KaOoXov.  EI(t\v  apn  dpx"-'^  ^ ^  ^^  »  crvWoyia-fios,  wv  ovk 
((TTi  u-vWoyiCTfXos'  inaytoyi]  apn. 

Aristotle's  Nicomachean  Ethics^  vi.  3  (3). 


Quamvis  ad  scientiam  (luamlibet  via  unica  pateat,  qua  nempe  a 
notioribus  ad  minus  nota  et  a  manifestis  ad  obscuriorum  notitiam 
progredimur,  atque  univcrsalia  nobis  prrccipue  nota  sint  (ab  univer- 
salibus  enim  ad  parlicularia  ratiocinando  oritur  scientia),  ipsa  tamen 
universalium  in  intellectu  comprehensio  a  singulariuro  in  sensibus 
nostris  perceptione  exsurgit. 

Preface  to  Harvey's  Treatise  De  Generatione  Animalium. 


ELEMENTS 


OF 


INDUCTIVE    LOGIC 


B 


*^*  The  notes  appended  to  the  Chapters  (as  dis- 
tinguished from  the  foot-notes)  are  designed  to  inform 
the  student  of  any  divergences  from  the  ordinary  mode 
of  treatment,  or  to  afford  him  information  on  disputed 
questions  which  it  appeared  inconvenient  to  notice  in  the 
text.     They  may  be  omitted  on  the  first  reading. 


CHAPTER   I. 


On  the  Nature  of  Inductive  Inference, 


'T^WO  bodies  of  unequal  weight  (say  a  guinea  and  a 
feather)  are  placed  at  the  same  height  under  the 
exhausted  receiver  of  an  air-pump.  When  released,  they 
are  observed  to  reach  the  bottom  of  the  vessel  at  the 
same  instant  of  time,  or,  in  other  words,  to  fall  in  equal 
times.  From  this  fact,  it  is  inferred  that  a  repetition  of 
the  experiment  either  with  these  two  bodies  or  with  any 
other  bodies  would  be  attended  with  the  same  result,  and 
that,  if  it  were  not  for  the  resistance  of  the  atmosphere 
and  other  impeding  circumstances,  all  bodies,  whatever 
their  weight,  would  fall  through  equal  vertical  spaces  in 
equal  times.  Now,  that  these  two  bodies  in  this  par- 
ticular experiment  fall  to  the  bottom  of  the  receiver  in 
equal  times  is  merely  a  fact  of  observation,  but  that  they 
would  do  so  if  we  repeated  the  experiment,  or  that  the 
next  two  bodies  we  selected,  or  any  bodies,  or  all  bodies, 
would  do  so,  is  an  inference,  and  is  an  inference  of  that 
particular  character  which  is  called  an  Inductive  In- 
ference or  an  Induction  \ 

*  The  student  must  throughout  bear  in  mind  the  ambiguous  use  of 
the  words  Induction,  Inference,  &c.,  as  signifying  both  the  result 
and  the  process  by  which  the  result  is  arrived  at.  See  Deductive 
Logicy  Preface,  and  Part  III.  ch.  i.  note  i. 

B  2 


NATURE  OF 


What  assumptions  underlie  this  inference,  and  on  what 
grounds  does  it  rest  ? 

My  object  in  placing  the  two  bodies  under  the  receiver 
was  obviously  to  answer  a  question  which  I  had  pre- 
viously addressed  to  myself:  viz.  whether,  when  subject 
to  the  action  of  gravity  ^  only,  they  would  fall  in  equal 
or  in  unequal  times.  By  exhausting  the  air  in  the  re- 
ceiver, I  am  able  to  isolate  the  phe?tometion,  and  thus,  by 
removing  all  circumstances  affecting  the  bodies,  except 
the  action  of  gravity,  to  watch  the  effect  of  this  cause 
operating  alone.  But  in  trying  this  experiment,  in  iso- 
lating the  phenomenon,  and  asking  what  will  be  the  effect 
of  the  action  of  gravity  operating  alone,  I  am  evidently 
assuming  that  the  effect,  whatever  it  may  be,  will  be 
entirely  due  to  the  cause  or  causes  which  are  then  and 
there  in  action  ;  in  other  words,  I  am  assuming  that 
nothing  can  happen  without  a  cause,  that  no  change  can 
take  place  without  being  preceded  or  attended  by  circum- 
stances which,  if  we  were  fully  acquainted  with  them, 
would  fully  account  for  that  change.  This  assumption 
(which  may  be  called  the  Laiv  of  Universal  Causation) 
is  universally  admitted  by  mankind,  or  at  least  by  the 
reflecting  portion  of  mankind,  though  the  grounds  on 
which  it  is  admitted  have  been  variously  stated;  some 

^  When  T  employ  the  expression  *  action  of  gravity '  or  *  force  of 
gravity,'  1  must  not  be  understood  as  adopting  any  particular  theory 
on  the  nature  of  the  phenomenon  which  we  call  '  gravitation.'  I 
use  these  terms  simply  because  they  are  short  and  recognised  phrases 
for  expressing  the  fact  that  all  terrestrial  bodies,  when  left  entirely 
free,  fall  in  the  direction  of  the  earth's  centre. 


INDUCTIVE  INFERENCE, 


justifying  it  by  an  appeal  to  the  continuous  and  uncon- 
tradicted experience  not  only  of  the  individual  himself 
but  of  the  human  race,  others  by  an  appeal  to  the 
necessities  of  thought. 

Thus  far,  however,  we  have  only  ascertained  that  the 
fact  of  these  two  particular  bodies,  in  this  particular 
instance,  falling  to  the  ground  in  equal  times  is  due  to 
the  action  of  gravity,  unimpeded  by  any  other  circum- 
stances. But  why  should  I  infer  that  they,  if  the  experi- 
ment were  repeated,  or  any  other  two  bodies,  if  exposed 
to  the  same  circumstances,  would  behave  in  the  same 
way  ?  It  is  not  enough  to  feel  assured  that  nothing  can 
happen  without  a  cause,  and  that  the  only  cause  operating 
in  this  particular  instance  is  the  action  of  gravity;  I  must 
also  feel  assured  that  the  same  cause  will  ^  invariably  be 
followed  by  the  same  effect,  or,  to  speak  more  accurately, 
that  the  same  cause  or  combination  of  causes,  will,  if 
unimpeded  by  the  action  of  any  other  cause  or  combina- 
tion of  causes,  be  invariably  followed  by  the  same  effect 
or  combination  of  effects,  or,  to  state  the  same  propo- 
sition in  somewhat  different  language,  that,  whenever  the 
same  antecedents,  and  none  others,  are  introduced,  the 
same  consequents  will  invariably  follow.  This  assump- 
tion (or  law)  is,  like  the  former,  universally  admitted  by 
mankind,  or  the  reflecting  portion  of  mankind,  though  the 
grounds  on  which  it  is  admitted  have  been  variously  stated, 

^  The  expression  *  will '  is  used  for  the  sake  of  brevity.  The 
argument,  however,  is  not  simply  from  the  present  to  the  future,  but 
from  cases  within  the  range  of  our  experience  to  all  cases,  past, 
present,  or  future,  without  that  range,     bee  p.  32,  note  31. 


6  NATURE   OF 

some,  as  in  the  case  of  the  former  law,  referring  it  to 
experience,  others  to  certain  necessities  of  thought  arising 
from  the  original  constitution  of  the  human  mind.  This 
law  may  be  called  the  Lmv  of  the  Uniformity  of  Nature'. 
The  argument,  then,  in  the  case  which  we  have  taken 
as  our  instance,  may  be  represented  as  follows  : — 

I  observe  that  these  two  bodies  (though  of  unequal 
weight)  reach  the  bottom  of  the  receiver  at  the 
same  moment. 
This  fact  must  be  due  to  some  cause  or  combination 

of  causes  (Law  of  Universal  Causation). 
The  only  cause  operating  in  this  instance  is  the 
action  of  gravity. 
,  • .  The  fact  that  these  two  bodies  reach  the  bottom  of 
the  receiver  at  the  same  moment  is  due  to  the 
action  of  gravity,  operating  alone. 
But,  whenever  the  same  cause  or  combination  of 
causes  is  in  operation,  and  that  only,  the  same 
effect  will  invariably  follow  (Law  of  Uniformity  of 
Nature). 

♦  It  is,  ])erhaps,  necessary  thus  early  to  warn  the  student  that  tlie 
converse  of  the  Law  of  the  Uniformity  of  Nature  does  not  hold  true. 
Though  the  same  cause,  that  is,  the  same  antecedent  or  combination 
of  antecedents,  is  never  followed  by  different  effects,  the  same  effect, 
or,  more  strictly  speaking  (see  pp.  127,  8),  the  same  portion  of  an 
effect,  may  be  due  to  different  causes.  We  can,  thus,  always  argue 
from  the  cause  to  the  effect,  but  we  cannot  always  argue  from  the 

effect  to  the  cause. 

The  Law  of  the  Uniformity  of  Nature  implies,  I  conceive,  the  truth 
of  the  law  of  the  Persistence  or  Conservation  of  Energy  (namely,  that 
no  cause,  or  part  of  a  cause,  will  ever  be  ineffective,  or,  in  other  words, 
that  no  energy  is  ever  lost\  and  hence  I  have  not  thought  it  necessary 
to  inUoduce  any  express  mention  of  this  latter  law  in  the  text. 


INDUCTIVE  INFERENCE.  7 

.  • .  Whenever  these  two  bodies,  or  any  other  two  or 
more  bodies  (even  though  of  unequal  weight),  are 
subject  to  the  action  of  gravity  only,  they  will  reach 
the  bottom  of  the  receiver  at  the  same  moment, 
or,  in  other  w^ords,  will  fall  in  equal  times. 

The  induction  just  examined  has  been  arrived  at  by  a 
process  of  elimination,  and  takes  for  granted  the  concep- 
tion of  causation.  It  is  representative  of  the  inductions 
with  which  science  is  mainly  concerned,  and  of  which  I 
shall  have,  for  the  most  part,  to  treat  in  the  present  work. 
But  there  are  other  inductions  of  a  simpler  character,  the 
validity  of  which  is  assured  not  by  any  artificial  process 
of  elimination,  but  merely  by  a  series  of  uncontradicted 
experiences.  This  kind  of  induction  is  usually  distin- 
guished by  logicians  as  Inductio  per  Enumerationem 
Simplicem,  It  is  often  (as  will  hereafter  be  pointed  out 
in  the  4th  chapter)  exceedingly  untrustworthy,  but,  when 
the  area  of  experience  is  very  wide,  the  evidence  which  it 
afTords  may  approach  to,  and  even  amount  to,  certainty. 
Often  moreover,  and  especially  in  the  case  of  our  widest 
generalisations,  it  is  our  only  resource. 

Amongst  inductions  of  this  kind  must  be  included,  as 
I  conceive,  the  Laws  of  Uniformity  of  Nature  and  Uni- 
versal Causation  themselves,  as  well  as  the  axioms  of 
mathematics  and  certain  facts  of  co-existence  which  have 
not  yet  been  resolved  into,  or  possibly  do  not  admit  of 
being  resolved  into,  facts  of  causation.  As  examples  of 
the  last  class  I  may  specify  the  co-existence  throughout 
matter  of  the  properties  of  inertia  and  gravity,  and  the 


8 


NATURE   OF 


\ 


co-inherence  of  attributes  in  the  various  kinds  of  animals, 
plants,  and  minerals,  as,  for  instance,  fusibility  at  a  certain 
point  together  with  a  certain  specific  gravity  in  gold,  or 
the  combination  of  rationality  with  a  peculiar  physical 
form  in  man.  Though  co-existing  facts  of  this  nature 
may  possibly  be  due  to  some  causal  connexion,  and 
might,  if  we  had  a  perfect  knowledge  of  all  natural  pro- 
cesses, be  explained  in  that  manner,  they  are,  as  yet, 
known  to  us  only  as  facts  of  co-existence,  and  established 
only  by  an  inductio  per  enumerationem  simplicem,  or 
uncontradicted  experience. 

Mr.  Bain*^  enumerates  three  kinds  of  uniformities,  which 
may  be  established  by  induction,  those  of  Co-existence, 
Causation,  and  Equality.  Uniformities  of  Co-existence 
and  Equality  can  be  established  only  by  Inductio  per 
Enumerationem  Simplicem,  while  those  of  Causation, 
though,  in  the  actual  state  of  our  knowledge,  they  often 
rest  only  on  this  evidence,  ought  always  to  be  established 
by  the  more  refined  methods  to  be  described  in  the 
sequel  of  this  book.  To  the  above  classification  I  ought 
lo  add  the  Laws  of  Uniformity  of  Nature  and  Universal 
Causation,  both  of  which,  as  already  remarked,  I  conceive 
to  be  established  by  uncontradicted  experience,  or,  in 
other  words,  by  an  Inductio  per  enumerationem  sim- 
plicem coextensive  with  all  human  knowledge  *.  These 
fundamental  laws,  thus  verified  by  a  constant  experience, 

^  Logic,  Bk.  III.  ch.  ii. 

*'  On  the  nature  of  the  evidence  on  which  these  laws  rest,  see  the 
third  appended  note  at  the  end  of  this  chapter. 


INDUCTIVE  INFERENCE.  9 

are  assumed  in  all  scientific  inductions  concerning  Caus- 
ation, whereas,  in  mere  inductions  per  Enumerationem 
Simplicem,  all  that  is  assumed  is  the  much  vaguer  and 
less  precise  belief  that,  under  similar  circumstances,  the 
unknown  resembles,  or  will  resemble,  the  known,  a 
belief  which  experience  shows  to  be  subject  to  many 
modifications ''. 

As  the  inductions  of  Causation  are  those  with  which 
science  is  mainly  concerned,  and  to  which  alone  the 
more  refined  rules  of  Inductive  Logic  are  applicable,  I 
shall  in  the  following  work  limit  myself  almost  entirely 
to  their  consideration.  The  inductions  of  Co-existence, 
with  which  I  shall,  to  some  extent,  be  concerned  in  the 
section  on  Classification,  I  shall  regard  as  subservient  to 
these  ^ 

From  what  has  been  said  above,  as  well  as  in  distin- 
guishing the  various  kinds  of  inference  in  the  Manual 
of  Deductive  Logic,  it  will  be  seen  that  Induction  may  be 
defined  as  the  legitimate  inferefice  of  the  unknown  from 
the  known,  that  is,  of  propositions  applicable  to  cases 
hitherto  unobserved  and  unexamined  from  propositions 
which  are  known  to  be  true  of  the  cases  observed  and 
examined.     Thus,  from  the   proposition  that   a  guinea 

'  This  belief  is  what  is  frequently  understood  by  the  Law  of  the 
Uniformity  of  Nature,  but  I  have  thought  it  desirable  to  confine  that 
expression  to  the  more  precise  statement  with  regard  to  the  uniform 
action  of  causes. 

*  I  shall  briefly  recur  to  the  subject  of  Inductions  of  Co-existence 
in  the  fourth  chapter,  under  the  head  of  Inductio ^er  Eniimcrationcftt. 
Simplicem. 


10 


NATURE  OF 


and  a  feather,  if  placed  under  the  exhausted  receiver  of 
an  air-pump,  will  fall  through  equal  vertical  spaces  in 
equal  times,   may  be   inferred   inductively  the  proposi- 
tion that  a  shilling,  a  penny,  and  a  straw  will,  if  exposed 
to  the  same  circumstances,  also  fall  in  equal  times.     But, 
as  we  can  only  draw  this  inference  on  grounds  which  are 
equally  applicable  to  all  bodies  whatsoever,  when  exposed 
to  the  same  circumstances,  and  as  we  might  make  the 
same  assertion  of  any  two  or  more  bodies,  and  conse- 
quently of  all  bodies,  it  will  be  seen  that  Induction  is 
not  only  an  inference  of  the  unknown  from  the  known  ; 
but,  in  virtue  of  that  fact,  of  the  general  from  the  particular. 
In  every  inductive  argument,  in  fact,  it  is  implied  that 
wherever  or  whenever  the   same   circumstances   are  re- 
peated, the  same  effects  will  follow.      Induction   may, 
therefore,  also  be  defined  as  the  legitimate  inference  of  the 
general  from  the  particular,  or  (in  order  to  include  those 
cases  where  general  propositions  are  themselves  employed 
as  the  starting-point  of  an  inductive  argument,  of  which 
numerous  instances  will  occur  as  we  proceed)  of  the  ?norc 
general  from  the  less  general '. 

'  This  is  a  better  and  more  accurate  definition  than  that  given  at 
the  beginning  of  the  paragraph,  because,  if  we  adopt  the  theory  thnt 
all  our  fundamental  beliefs  are  derived  from  experience,  there  is  no 
kind  of  inference  which  does  not  involve  the  assumption  that  we 
may  argue  from  the  known  to  the  unknown,  and  from  the  past  to 
the  present  and  the  future.  In  the  case  of  some  of  these  beliefs, 
however,  as  the  so-called  *  laws  of  thought,'  and  the  belief  in  the 
trustworthiness  of  our  present  consciousness  and  of  memory,  the 
assumption  has  been  made  so  often  and  so  constantly  that  we  have 
almost  ceased  to  be  conscious  of  making  it. 


INDUCTIVE  INFERENCE, 


IT 


In  trying  the  experiment  which  furnished  our  instance 
at  the  beginning  of  the  chapter,  we  were  attempting  to 
find   an    answer   to   the    question,  *  Do    bodies,    when 
subject  to  the  action  of  gravity  only,  fall  through  equal 
vertical  spaces  in    equal  or  in    unequal  times?'      The 
experiment  may  be  regarded  as  an   attempt  to  decide 
between  two  rival  theories  (or  hypotheses,  as  they  are  usu- 
ally called),  one  being  that  bodies  fall  quicker  in  propor- 
tion to  their  weights,  the  other  that  the  weight  of  the  body, 
when  the  resistance  of  the  atmosphere  is  removed,  does 
not  affect  the  time  of  falling.     The  experiment  is  decisive 
in  favour  of  the  latter  hypothesis,  which  is  thus  entitled 
to  rank  as  a  valid  induction.     Our  inductions  are  often, 
as  in  this  case,  the  result  of  an  attempt  to  decide  between 
rival  hypotheses,  or  a  reply  to  the  question  whether  some 
particular  hypothesis  be  true  or  not,  the  hypothesis  or 
hypotheses  suggesting  the  particular  experiment  to   be 
tried.     Sometimes,  however,  we  have   no  assistance  of 
this  kind,  and  we  try  experiments  simply  '  to  see  what 
will  come  of  them.'     Thus,  if  a  chemist  discovers  a  new 
element,  he  will  proceed  to  try  a  variety  of  experiments 
in  order  to  determine  the  proportions  in  which  it  will 
combine  with  other  elements,  as  well  as  to  discover  the 
various   properties    of   such   combinations.     Supposing 
the  experiments  to  have  been  properly  conducted,  the 
inductions  at  which  he  arrives  will   be  perfectly  valid, 
though  he  may  have  formed  no  previous  theories  as  to  the 
results  of  his  researches.     Occasionally,  too,  an  induction 
will  not  be  the  result  of  any  definite  course  of  investi- 


la 


NATURE  OF 


gation,  but  will  be  obtruded  on  our  notice,  as  in  the 
following  instance,  adduced  by  Sir  John  Herschel,  to 
show  that  '  after  much  labour  in  vain,  and  groping  in  the 
dark,  accident  or  casual  observation  will  present  a  case 
which  strikes  us  at  once  with  a  full  insight  into  a  subject.' 
*  The  laws  of  crystallography  were  obscure,  and  its  causes 
still  more  so,  till  Haiiy  fortunately  dropped  a  beautiful 
crystal  of  calcareous  spar  on  a  stone  pavement,  and 
broke  it.  In  piecing  together  the  fragments,  he  observed 
their  facets  not  to  correspond  with  those  of  the  crystal  in 
its  entire  state,  but  to  belong  to  another  form  ;  and  follow- 
ing out  the  hint thus  casually  obtruded  on  his 

notice,  he  discovered  the  beautiful  laws  of  the  cleavage, 
and  the  primitive  forms  of  minerals  '^' 

Thus,  we  perceive  that  our  inductions  are  sometimes 
preceded  by  hypotheses,  at  other  times  not.  In  most 
cases,  probably,  we  have  formed  some  supposition  (or 
hypothesis)  as  to  the  character  of  a  phenomenon  before 
we  enter  upon,  or,  at  least,  before  we  complete,  its  in- 
vestigation. Such  suppositions  (or  hypotheses)  are  often 
of  the  utmost  service  in  directing  the  course  which  our 
experiments  and  observations  shall  take.  Frequently, 
also,  it  is  impossible  to  perform  any  experiment,  or  to 
institute  any  series  of  observations,  which  shall  be  de- 
cisive of  the  question  before  us.  In  this  case,  unless 
we  altogether  suspend  our  judgment,  we  must  rest  con- 
tent with  an  unproved  theory,  and  it  becomes  of  prime 
importance  to  determine  to  what  conditions  such  a 
*"  W^t&^qV^  Discourse  on  the  Study  of  Xatural  Philosophy ^  §  191. 


INDUCTIVE  INFERENCE, 


13 


theory ",  supposition,  or  hypothesis  must  conform  in 
order  to  entitle  it  to  rank  as  a  probable  or  possible 
solution  of  our  difficulties.  A  subsequent  section  wmU 
be  specially  devoted  to  these  questions,  but  meanwhile 
it  seemed  desirable  at  once  to  direct  the  attention  of  the 
student  to  the  distinction  between  hypothesis  and  in- 
duction. He  must  bear  in  mind  that,  though  the  forma- 
tion of  hypotheses  is  frequently  an  important  step  in  the 
inductive  process,  a  hypothesis  must  be  carefully  dis- 
tinguished from  a  valid  induction.  Without  at  present 
attempting  any  formal  definition  of  a  hypothesis,  it  may 
be  distinguished  from  an  induction  (that  is,  a  valid, 
complete,  or  perfect  induction)  as  a  mere  supposition 
or  assumption  from  an  ascertained  truth. 

*^*  The  word  ^  cause '  is  commonly  used  in  a  verj- 
vague  and  indefinite  sense.  Of  the  various  antecedents 
whose  presence  or  absence  is  essential  to  the  event,  it 
is  usual  to  single  out  one  as  the  Cause,  and  either  to 
overlook  the  others,  or  to  speak  of  them  as  *  conditions.' 
Strictly  speaking,  however,  the  Cause  consists  in  the  pre- 
sence of  all  those  antecedents,  the  withdrawal  of  any  of 
which,  and  in  the  absence  of  all  those  antecedents,  the 
introduction  of  any  of  which,  might  frustrate  the  event. 
Thus,  to  take  the   homely  instance  of  lighting  a  fire. 


"  The  word  *  theory '  is,  unfortunately,  employed  in  two  mean- 
ings :  (i)  as  =  hypothesis,  as  when  we  speak  of  the  undulatory 
theory,  the  Darwinian  theory,  or  two  or  more  *  rival  theories' ;  (2) 
as  an  ascertained  truth,  or  body  of  truths,  as  when  we  speak  of  the 
*  lunar  theory/  or  the  *  theory  of  equations.* 


u 


NATURE  OF 


The  application   of  the   lighted   match  is  what  would 
ordinarily  be  called  the  cause  of  the  combustion.     But 
there  are  other  conditions  equally  necessary,  as,  for  in- 
stance, amongst  the  positive  conditions,  the  presence  of 
fuel  and  of  atmospheric  air,  and,  amongst  the  negative 
conditions,  the  absence  of  such  a  quantity  of  moisture 
as  would  prevent  the  fuel  from  igniting.     In  assigning 
the  cause  of  a  phenomenon,  it  is  seldom  that  the  nega- 
tive conditions  are  mentioned.     It  is  generally  under- 
stood that  we  assign  a  cause,  subject  to  the  qualification 
'  no   counteracting   cause    intervening.'      Amongst   the 
positive  conditions,  we  usually  select  that  which,  being 
last  introduced,  completes  the  assemblage  of  conditions, 
and  stands  in  closest  proximity  to  the  effect.     Thus, 
in  our  example,  the  combustion  is  said  to  be  due  to 
the  application  of  the  match,  and,  when  a  man,  who  has 
j)reviously  been  in  a  bad  state  of  health,  is  attacked 
by   a   fever,  we   speak   of  the   fever  as   the   cause   of 
his  death.      These,  however,  as  observed  by  Mr.  Mill, 
are   by  no  means  invariable   rules.      *  It  must   not  be 
supposed  that  in  the  employment  of  the  term  this  or 
any  other  rule  is  always  adhered  to.     Nothing  can  better 
show  the  absence  of  any  scientific  ground  for  the  dis- 
tinction  between  the  cause  of  a  phenomenon  and  its 
conditions,  than   the   capricious   manner    in  which  we 
select  from  among  the  conditions  that  which  we  choose 
to  denominate  the  cause.     However  numerous  the  con- 
ditions may  be,  there  is  hardly  any  of  them  which  may 
not,  according   to  the   purpose  of  our  immediate   dis- 


INDUCTIVE  INFERENCE. 


15 


course,  obtain  that  nominal  pre-eminence.'  Thus,  if  a 
plot  of  dry  heath  is  ignited  by  a  spark  from  a  railway- 
engine,  we  may,  in  common  parlance,  attribute  the  fire 
either  to  the  spark,  or  to  the  dryness  of  the  heath,  or  to 
the  ill-construction  of  the  engine ;  the  first  of  these 
assigned  causes  being  the  proximate  event,  the  second 
one  of  the  other  positive  conditions,  the  last  a  negative 
condition.  What,  when  employing  popular  language, 
we  dignify  with  the  name  of  Cause  is  that  condition 
which  happens  to  be  most  prominent  in  our  minds  at 
the  time.  It  is,  perhaps,  superfluous  to  add  that,  when 
aiming  at  scientific  accuracy,  we  ought  to  enumerate 
all  the  conditions,  or,  at  least,  all  the  positive  conditions, 
on  which  a  phenomenon  depends,  unless  we  have  a  right 
to  presume  that  there  is  no  likelihood  of  their  being 
overlooked  by  those  whom  we  address  '^ 

In  the  science  of  Medicine,  the  cause  which  com- 
pletes the  assemblage  of  conditions  is  often  distinguished 
as  the  exciting  cause,  the  other  causes  being  called /r^- 
disposing.  Thus,  the  peculiarities  of  constitution,  age, 
sex,  occupation,  &:c.,  which  render  a  person  more  than 
ordinarily  liable  to  any  particular  disorder,  would  be 
called  ihQ  pre-disposing  causes  ;  the  contagion  (by  which 
the  body  is  brought  into  contact  with  some  specific 
poison),  a  sudden  chill,  bodily  fatigue,  mental  depres- 
sion, or  any  circumstance,  on  the  supervention  of  which 
the  disease  is  immediately  consequent,  would  be  called 

"  The  subject  of  this  paragraph  is  treated  with  great  ability  in 
Mr.  Mill's  Logic,  Bk.  III.  ch.  v.  §  3. 


i6 


NATURE  OF 


the  exciting  cause  ".  The  pre-disposing  causes  of  Asiatic 
Cholera,  for  instance,  are  enumerated  in  Dr.  Guy's  edition 
of  Dr.  Hooper's  *  Vade  Mecum,'  as  *  debih'ty  ;  impaired 
health  ;  intemperance ;  impure  air  ;  low  and  damp  situa- 
tions ;  the  summer  and  autumn  seasons  :  the  exciting 
causes  as  contagion ;  a  peculiar  poison  diffused  through 
the  atmosphere.'  The  importance  of  attending  to  this 
distinction  in  historical  and  political  investigations  is 
forcibly  stated  and  illustrated  by  Sir  G.  C.  Lewis,  in 
his  Methods  of  Observation  and  Reasoning  in  Politics, 
vol.  i.  ch.  ix.  p.  333,  &c. 

^fjte  i^— Mr.  Mill  {Logic,  Book  II.  ch.  iii.)  maintains 
that,  in  an  act  of  induction  we  usually,  though  not  in- 
variably, argue  directly  from  one  particular  case  to  an- 
other. Dr.  Whewell,  on  the  other  hand,  holds  that  all 
inductive  inference  is  from  the  particular  to  the  general. 
{Philosophy  of  Discovery,  ch.  xxii.  §  1-14)  Though 
I  have  adopted  Dr.  Whewell's  language  (which  is  that 
ordinarily  employed),  I  cannot  recognise  the  importance 
of  the  difference  which  he  believes  to  exist  between 
himself  and  Mr.  Mill.  To  say  that  what  I  find  to  be 
true  of  this  case  will  be  true  of  the  next  which  resembles 
it  in  certain  assignable  respects,  whatever  that  case  may 
be,  or  that  what  I  found  to  be  true  of  that  case  must  be 
true  of  this,  because  this  resembles  that  in  certain  as- 

»'  See  Dr.  Watson's  Lectures  on  Physic y  Lecture  VI. 

"  The  student,  unless  he  have  some  previous  acquaintance  with 
the  subjects  discussed  in  them,  is  recommended  to  omit  these  notes 
on  the  first  reading. 


INDUCTIVE  INFERENCE. 


17 


signable  respects,  is  virtually  to  say  that  it  is  true  of  any 
and  every  case  which  presents  these  points  of  resem- 
blance. What  is  true  of  each  or  any  case,  taken  in- 
differently, must  be  true  of  all.  '  The  burnt  child  dreads 
the  fire.'  Why?  Because  it  once  suffered  pain,  from 
burning  its  finger.  Now,  it  appears  to  me  indifferent 
whether  we  represent  the  child  as  having  in  its  mind 
the  proposition  *  That  object  causes  pain,'  or  the  pro- 
position *That  object  will  cause  me  pain  now,  if  I  ap- 
l)roach  too  near  to  it.'  But,  as  the  former  (the  general) 
inference  seems  to  be  virtually  implied  in  the  latter  (the 
particular),  and,  as  Mr.  Mill  acknowledges,  the  particular 
inference  can,  on  reflexion,  only  be  justified  by  granting 
the  truth  of  the  general  one,  I  prefer  adhering  to  the 
common,  and,  as  I  think,  the  more  intelligible  account 
of  induction.  Mr.  Mill  himself,  in  one  place,  speaks 
of  Induction  as  '  generalisation  from  experience,'  and, 
in  another,  as  *  the  inference  of  a  more  general  from 
less  general  propositions  ^V 

Though  agreeing  with  Dr.  Whewell  in  his  main 
position,  I  must  express  my  entire  dissent  from  the  dis- 
tinction which,  throughout  this  discussion,  he  attempts 
to  draw  between  our  reasonings  in  the  ordinary  affairs 

^'  Mr.  Jevons  {Principles  of  Science^  vol.  i.  pp.  261,  262)  seems  to 
have  sli<;htly  misapprehended  my  meaning  in  this  note.  While  I 
believe  that  we  do,  as  a  matter  of  fact,  often  argue  from  particular 
to  particular.  I  entirely  agree  with  Mr.  Jevons  {Principles  of  Science, 
vol.  ii.  p.  243)  in  holding  thnt  'what  is  inf.rrcd  of  a  particular  case 
might  be  inferred  of  all  similar  cases,'  or,  in  other  words,  that  ihaloj^ical 
JHstifcation  of  such  inferences  is  to  be  found  in  the  general  staten.ent. 


i8 


NATURE   OF 


of  life  and  Induction  as  employed  in  scientific  research. 
However  various  may  be  the  conditions  of  their  applica- 
tion, I  cannot  but  regard  the  mental  processes  as  iden- 
tical, on  whatever  classes  of  objects  they  may  be 
exercised.  We  may  meet  with  insurmountable  difficulties 
in  the  attempt  to  apply  Induction  to  some  obscure 
question  of  Physiology,  and  we  may  employ  it  with  ease 
and  success  a  hundred  times  a  day  in  compassing 
pleasure  or  avoiding  pain,  but  I  believe  the  mental 
process  to  be  essentially  the  same  in  both  cases. 

jSfote  2.— Since  the  time  of  Hume,  the  nature  of  our 
conception  of  Cause  has  formed  one  of  the  chief  topics 
of  philosophical  controversy.  Previously  to  his  time,  it 
appears  to  have  been  taken  for  granted  by  the  great 
majority  of  modern  philosophers  of  all  schools  '*  (if  we 
except  those  who,  like  Malebranche,  believed  God  to  be 
the  only  efficient  cause  in  the  universe,  and  so-called 
acts  of  causation  to  be  only  the  occasions  of  the  Divine 
interference'"),  that  the  idea  of  causation  necessarily 
implies    the    idea    of  power    or    necessary    connexion; 

"  Dugald  Stewart  (in  his  Philosophy  of  the  Human  Mind,  Notes 
C  and  MM)  has  certainly  succeeded  in  showing  that  Hume's  views 
on  the  nature  of  Cause  were  anticipated  by  casual  remarks  of  several 
other  writers  ;  but  it  still  remains  true  that  Hume  was  the  first 
philosopher  who   definitely   attacked   the   prevalent    philosophical 

theory. 

"  Still,  even  according  to  these  philosophers,  every  act  of  causa- 
tion implies  an  act  of  power ;  only  the  power  is  exerted  not  by  the 
so-called  cause,  but  by  the  Deity  himself.     It  will  be  noticed  that  I 
speak  only  of  modern  philosophers.     Into  the  difficult  question  of 
the  notions  of  causation  entertained  by  ancient  writers  I  do  not  enter. 


INDUCTIVE  INFERENCE. 


19 


necessary  connexion,  that  is  to  say,  between  the  cause  and 
effect,  or  power  in  the  cause  to  produce  the  effect.  Even 
Locke,  who  effected  a  revolution  in  modern  philosophy, 
left  this  idea  of  Power  unassailed,  though  he  attempted 
to  account  for  its  formation.  'The  mind,'  says  he  ^^ 
*  being  every  day  informed,  by  the  senses,  of  the 
alteration  of  those  simple  ideas  it  observes  in  things 
without ;  and  taking  notice  how  one  comes  to  an  end, 
and  ceases  to  be,  and  another  begins  to  exist,  which 
was  not  before;  reflecting  also  on  what  passes  within 
itself,  and  observing  a  constant  change  of  its  ideas, 
sometimes  by  the  impression  of  outward  objects  on  the 
senses,  and  sometimes  by  the  determination  of  its  own 
choice ;  and  concluding  from  what  it  has  so  constantly 
observed  to  have  been,  that  the  like  changes  will  for  the 
future  be  made,  in  the  same  things,  by  like  agents,  and 
by  the  like  ways,  considers  in  one  thing  the  possibility  of 
having  any  of  its  simple  ideas  changed,  and  in  another 
the  possibility  of  making  that  change ;  and  so  comes  by 
the  idea  which  we  call  Power.  Thus  we  say,  fire  has  a 
power  to  melt  gold,  i.e.  to  destroy  the  consistency  of 
its  insensible  parts,  and  consequently  its  hardness,  and 
make  it  fluid  ;  and  gold  has  a  power  to  be  melted  :  that 
the  sun  has  a  power  to  blanch  wax,  and  wax  a  power  to 
be  blanched  by  the  sun,  whereby  the  yellowness  is  de- 
stroyed, and  whiteness  made  to  exist  in  its  room.  In 
which,  and  the  like  cases,  the  power  we  consider  is  in 
reference  to  the  change  of  perceivable  ideas.     For  we 

"  Locke's  Essay y  vol.  ii.  ch.  xxi.  §  i. 
C  2 


20 


NATURE  OF 


cannot  observe  any  alteration  to  be  made  in,  or  operation 
upon  anything,  but  by  the  observable  change  of  its 
sensible  ideas  ;  nor  conceive  any  alteration  to  be  made, 
but  by  conceiving  a  change  of  some  of  its  ideas.'  He 
then  proceeds  to  include  our  idea  of  Power  amongst  ouf 

Simple  Ideas. 

Hume  contested  the  validity  of  this  idea  by  an  appeal 
to  experience.      Whence  do  we  obtain    this  notion   of 
necessary  connexion  between  two  events?     Do  we  ob- 
serve any  such  connexion  in  the  events  which  take  ])lace 
in  the  external  world,  or  in  the  relation  between  volition 
and  the  motion  of  the  organs  of  the  body,  or  in  the  act 
of  the  will    by  which   it    summons    up,   dwells  on,  or 
dismisses  ideas  ?     '  We  have  sought  in  vain  for  an  idea 
of  power  or  necessary  connexion,  in  all  the  sources  from 
which  we  could  suppose  it  to  be  derived.     It  appears 
that,  in  single  instances  of  the  operation  of  bodies,  we 
never  can,  by  our  utmost  scrutiny,  discover  anything  but 
one   event   following   another ;    without   being   able   to 
comprehend   any  force  or  power,  by  which    the   cause 
operates,  or  any  connexion  between  it  and  its  supposed 
effect.     The  same  ditTiculty  occurs  in  contemplating  the 
operations    of  mind   on   body,  where  we   observe   the 
motion  of  the  latter  to  follow  upon  the  volition  of  the 
former,  but  are  not  able  to  observe  or  conceive  the  tie, 
which  binds  together  the  motion   and  volition,  or  the 
energy  by  which  the  mind  produces  this  effect.     The 
authority  of  the  will  over  its  own  faculties  and  ideas  is 
not  a  whit   more  comprehensible  :    so   that,   upon    the 


INDUCTIVE  INFERENCE, 


21 


whole,  there  appears  not,  throughout  all  nature,  any  one 
instance  of  connexion,  which  is  conceivable  by  us.  All 
events  seem  entirely  loose  and  separate.  One  event 
follows  another ;  but  we  never  can  observe  any  tie  be- 
tween them.  They  seem  conjoined^  but  never  connected. 
And  as  we  can  have  no  idea  of  anything,  which  never 
appeared  to  our  outward  sense  or  inward  sentiment,  the 
necessary  conclusion  seems  to  be,  that  we  have  no  idea 
of  connexion  or  power  at  all,  and  that  these  words  are 
absolutely  without  any  meaning,  when  employed  either 
in  philosophical  reasonings,  or  common  life^^'  Does 
Hume  then  deny  thenar/  of  causation^  namely,  that,  when 
we  have  been  accustomed  to  observe  one  event  invari- 
ably followed  by  another,  we  may  confidently  expect, 
other  circumstances  remaining  the  same,  that  the  one 
will  continue  to  be  followed  by  the  other  in  the  future, 
and  that,  if  we  perceive  a  change  in  any  phenomenon, 
we  may  be  confident  that  some  other  event  has  pre- 
ceded that  change  ?  Certainly  not.  There  is,  in  Hume's 
writings,  absolutely  no  foundation  for  the  virulence  with 
which  he  is  attacked   :  y  Reid  '^     What    he   called   in 

^^  Hume's  Essays.     Essa}  on  the  Idea  of  Necessary  Causation. 

^^  The  followin^r  may  serve  as  a  specimen  of  Keid's  diatribes 
against  Hume.  'Of  all  the  paradoxes  this  author  has  advanced, 
there  is  not  one  more  shocking  to  the  human  understanding  than 
this,  That  things  may  begin  to  exist  without  a  cause.  This  would 
put  an  end  to  all  speculation,  as  well  as  to  all  the  business  of  life. 
The  employment  of  speculative  men,  since  the  beginning  of  the 
world,  has  been  to  investigate  the  causes  of  things.  What  pity  is  it, 
they  never  thought  of  putting  the  previous  question,  Whether  things 
have  a  cause  or  not  ?    This  question  has  at  last  been  started ;    and 


22 


NATURE   OF 


question  was  not  the  in  variableness  of  the  fact  of  causa- 
tion, but  the  grounds  of  the  prevalent  notions  attached 
to  the  word  Cause.  Whether  his  speculations  on  this 
subject  be  well  or  ill-founded,  he  certainly  did  not  deny 
the  correctness  of  the  principles  on  which  men  act  in 
ordinary  life  or  which  guide  them  in  scientific  research. 

There  is  another  objection  to  the  statements  contained 
in  Hume's  Essay  which  is  better  founded  than  the  fore- 
going. If  the  term  'cause'  be  convertible  with  the  term 
*  invariable  antecedent,'  it  has  been  justly  objected  by 
Reid'^*  that  we  might  speak  of  day  as  the  cause  of  night, 
and  of  night  as  the  cause  of  day.  That  there  are  ex- 
pressions in  the  Essay,  in  which  the  cause  seems  to  be 
absolutely  identified  with  the  invariable  antecedent  or 
the  sum  of  the  invariable  antecedents,  cannot  be  denied. 
Such   is   the   following :    '  Suitably   to   this   experience, 

what  is  there  so  ridiculous  as  not  to  be  maintained  by  some  phi- 
losopher ? ' — Active  Powers,  Essay  I.  ch.  iv.  Sir  W.  Hamilton  and 
Dr.  Mansel  take  a  far  juster  view  of  Hume's  position.  Even  Sir  W. 
Hamilton,  however,  in  commenting  on  Reid's  statement, s;iys,  '  This' 
(namely,  That  things  may  begin  to  exist  without  a  cause)  *  is  not 
Hume's  assertion  ;  but  that,  on  the  psychological  doctrine  generally 
admitted,  we  have  no  valid  assurance  that  they  may  not.'  The 
latter  is,  certainly,  not  Hume's  assertion.  It  is  true  that  he  bases 
the  notion  of  causation  on  experience,  but  then  he  regards  experience 
as  the  sole  source  of  all  our  knowledge,  other  than  that  of  mathe- 
matics. Sir  William  Hamilton's  note  requires  only  to  be  compared 
•with  the  follov\ing  passage  from  the  Essay:  'But  when  one  par- 
ticular species  of  event  has  always,  in  all  instances,  been  conjoined 
with  another,  we  make  no  longer  any  scruple  of  foretelling  one  upon 
the  appearance  of  the  other,  and  of  employing  that  reasoning  which 
can  alone  assure  us  of  any  matter  of  fact  or  existence.' 
^  Active  rowers,  Essay  IV.  ch.  iii. 


INDUCTIVE  INFERENCE. 


23 


therefore,  we  may  define  a  cause  to  be  an  object,  fol- 
lowed by  another,  and  when  all  the  objects,  similar  to 
the  first,  are  followed  by  objects  similar  to  the  second.' 
But  then  the  sentence  proceeds :  '  Or,  in  other  words, 
7vherey  if  the  first  object  had  not  been,  the  second  never  had 
existed.^  Now  this  alternative  definition  is  not  open  to 
Reid's  objection  ^^,  though  it  is  open  to  the  objection  of 
ignoring  the  fact  that  the  same  event  may  be  due  to 
distinct  causes,  as  pointed  out  in  p.  6,  n.  4'-^'.  When 
modified  to  meet  this  objection,  it  would  run  thus : 
'Cause  [or  causes]  and  Effect  are  two  [or  more]  events, 
or  sets  of  events,  which  are  so  related,  that,  if  the  first 
[or  one  of  the  first]  had  not  been,  the  second  had  never 
existed.'  Or,  perhaps,  it  might  be  more  simply  stated 
thus :  *  An  Effect  is  so  related  to  its  Cause  or  its  alter- 
native Causes,  that  if  the  latter  or  one  of  the  latter  had 
not  been,  the  former  had  never  existed  ^^' 

2'  The  alternative  definition,  however,  introduces  a  new  idea,  not 
contained  in  the  first  definition,  that  oi  dependence  of  the  effect  upon 
the  cause,  which  it  is  not  easy  to  distinguish  from  the  idea  of  neces- 
sary connexion.  Hence,  Hume  appears  unconsciously  to  recur  to 
the  very  position  which  he  is  attacking.  It  seems  to  me  that  the 
relation  of  cause  and  effect,  or  the  dependence  of  effect  on  cause,  is 
an  idea  sui  generis,  and  cannot  be  resolved  into  the  mere  idea  of 
time,  or  antecedence  and  consequence.  The  introduction  of  the 
word  *  power,'  however,  or  even  of  the  word  '  necessary,'  into  the 
statement  of  the  relation,  occasions  needless  obscurity  and  difficulty. 

**  I  am  indebted  to  Professor  Park  of  Belfast  for  drawing  my 
attention  to  this  objection,  which  had  escaped  my  notice  in  the  First 
Edition.  It  was  originally  pointed  out  by  Dr.  Thomas  Brown,  in  his 
Enquiry  into  the  Relation  of  Cause  and  Effect,  Note  A. 

=*  This  definition  is,  it  must  be  confessed,  somewhat  deficient  in 


24 


NATURE   OF 


Both  Dr.  Thomas  Brown  and  Mr.  Mill  attempt  to  meet 
Raid's  objection. 

Brown  holds  that  the  cause  is  that  invariable  ante- 
cedent which  ifnmediaie/y  precedes  the  effect ;  thus  the 
position  of  the  sun  at  a  given  moment,  that  which  we 
call  sun-rise,  is  the  cause  of  day. 

Mill  attempts  to  meet  the  same  objection  by  having 
recourse  to  the  idea  of  '  uficonditionalness.^  The  cause 
of  a  phenomenon  is  '  the  antecedent  or  concurrence  of 
antecedents  on  which  it  is  invariably  and  unco7iditiotially 
consequent,'  i.e.  which  not  only  invariably  precedes  it, 
but  which  is  followed  by  the  effect  without  the  occur- 
rence of  any  other  condition.  Now  night  cannot  be 
called  the  cause  of  day,  because  it  might  go  on  for  ever 
without  being  followed  by  day,  unless  the  condition 
of  the  sun  rising  were  fulfilled.  See  Mill's  Logic^  Bk. 
III.  ch.  V.  §  5. 

simplicity.  But  I  venture  to  suggest  that  it  will  bear  closer  ex- 
amination than  that  of  Mr.  Mill,  who  defines  *  cause'  as  the  '  uncon- 
tlitional  invariable  antecedent.'  Whether  by  the  term  'unconditional* 
he  means  *  not  depending  on  any  previous  condition,'  or  '  not  com- 
bined with  any  concurrent  condition,'  it  may  be  objected  that  there 
is  no  such  phenomenon  ip  nature.  If,  as  seems  clear  from  the  con- 
text, the  term  be  used  in  the  latter  sense,  we  shall  not  only  be  ex- 
cluded from  saying  that  night  is  the  cause  of  day,  but  also  that  solar 
light  is  the  cause  of  day,  for  there  are  other  conditions,  both  positive 
and  negative,  essential  to  the  production  of  what  we  call  day  by  the 
solar  rays.  In  fact,  according  to  the  terms  of  this  definition,  we 
cDuld  never,  as  we  are  constantly  doing,  single  out  any  one  prominent 
phenomenon,  and  call  it  the  cause  of  an  event,  without  enumerating 
ail  the  other  conditions,  positive  and  negative,  which  are  essential 
to  its  operation. 


INDUCTIVE  INFERENCE, 


25 


The  objection  to  Brown's  account  is  that  we  frequently 
speak  without  hesitation  of  A  as  the  cause  of  B,  though 
we  are  by  no  means  certain  that  it  is,  strictly  speaking, 
the  immediate  antecedent  of  B,  nothing  else  whatever 
intervening  ;  in  fact,  it  is  questionable  whether  in  any 
case  we  can  ascertain  to  a  certainty  that  nothing  else 
intervenes  between  two  events.  Similarly,  it  may  be 
objected  to  Mill's  account  that  we  frequently  speak  with- 
out hesitation  of  A  as  being  the  cause  of  B,  though  we 
are  by  no  means  certain  that  there  are  not  other  ante- 
cedent conditions,  positive  and  negative,  which  must  be 
satisfied  before  A  can  be  followed  by  B  ;  and,  indeed, 
as  in  the  former  case,  it  may  be  questioned  whether  we 
can  ever  be  certain  that  there  are  no  other  conditions 
besides  those  which  we  have  selected  "^ 

The  first  author  of  eminence  who  adopted  Hume's 
view  of  the  nature  of  Cause  was  Dr.  Thomas  Brown  ; 
singularly  enough,  however,  so  far  from  assuming  with 
Hume  that  its  origift  was  to  be  found  in  experience,  he 
regarded  it  as  instinctive.  The  notion  of  '  Power '  he 
supposed  was  simply  a  gratuitous  hypothesis,  needlessly 
interpolated  between  the  antecedent,  which  we  call  the 
Cause,  and  the  consequent,  which  we  call  the  Effect. 
'  We  are  eager  to  supply,  by  a  little  guess-work  of  fancy, 
the  parts  unobserved,  and  suppose  deficiencies  in  our 
observation  where  there  may  truly  have  been  none  ;  till 
at  length,  by  this  habitual  process,  every  phenomenon 

^'^  It  is  curious  that  Mill,  in  attempting  to  answer  Keid,  takes  no 
notice  of  Brown's  answer. 


26 


NATURE   OF 


becomes,  to  our  imagination,  the  sign  of  something 
intermediate  as  its  cause,  the  discovery  of  which  is  to 
be  an  explanation  of  the  phenomenon.  The  mere 
succession  of  one  event  to  another  appears,  to  us,  very 
difficult  to  be  conceived,  because  it  wants  that  inter- 
vening something  which  we  have  learned  to  consider 
as  a  cause :  but  there  seems  to  be  no  longer  any  mystery, 
if  we  can  only  suppose  something  intervening  between 
them,  and  can  thus  succeed  in  doubling  the  difficulty, 
which  we  flatter  ourselves  with  having  removed  ;  since, 
by  the  insertion  of  another  link,  we  must  now  have  two 
sequences  of  events  instead  of  one  simple  sequence  '^^' 
Hume's  position  is  also  accepted  by  James  Mill  in  his 
Analysis  of  the  Phenomena  of  the  Human  Mind,  and  by 
John  Stuart  Mill  in  his  System  of  Logic, 

Hume's  antagonists  have  generally  (with  Kant)  com- 
bated his  arguments  by  denying  the  assumption  on  which 
they  are  based,  namely,  that  the  origin  of  our  conception 
of  Cause  is  to  be  sought  in  experience.  Hume,  it  will  be 
recollected,  challenges  those  who  maintain  the  hypothesis 
of  'power'  or  *  necessary  connexion'  to  show  how  we 
can  have  become  acquainted  with  it.  Does  it  come  from 
our  experience  of  the  external  world,  or  from  our 
experience  of  the  control  of  our  will  over  our  own  acts  or 
our  own  thoughts  ?  The  answer  of  the  Kantian  School 
would  be  that  it  does  not  come  from  experience  at  all, 
that  it  is  one  of  those  fundamental  conceptions  which 

2*  Brown's  Lectures  on  the  Philosophy  of  the   Human  Mind, 
Lecture  IX.     Cp.  Lecture  IL 


INDUCTIVE  INFERENCE, 


27 


are  native  to  the  human  mind,  not  given  by  experience 
but  evoked  by  it.  Others,  like  Reid  and  Stewart,  to 
whom  we  may  add  M.  Maine  de  Biran,  surrender  the 
notion  of  power  as  applied  to  causation  in  the  external 
world,  while  they  maintain  it  as  applied  to  our  own 
actions,  which  are  the  results  of  will.  We  are  conscious, 
they  say,  of  power  in  ourselves,  though  we  perceive  only 
succession  in  the  external  world.  Dr.  Mansel,  following 
Cousin,  adopts  a  third  view,  and  maintains  that  the 
notion  of  *  Power  '  is  given  only  in  the  control  of  the  mind 
over  its  own  operations.  *  The  intuition  of  Power  is  not 
immediately  given  in  the  action  of  matter  upon  matter ; 
nor  yet  can  it  be  given  in  the  action  of  matter  upon 
mind,  nor  in  that  of  mind  upon  matter  ;  for  to  this  day 
we  are  utterly  ignorant  how  matter  and  mind  operate 
upon  each  other.  We  know  not  how  the  material 
refractions  of  the  eye  are  connected  with  the  mental 
sensation  of  seeing,  or  how  the  determination  of  the  will 
operates  in  bringing  about  the  motion  of  the  muscles. 

We  can  investigate  severally  the  phenomena  of  matter 
and  of  mind,  as  we  can  examine  severally  the  constitu- 
tion of  the  earth,  and  the  architecture  of  the  heavens : 
we  seek  the  boundary  line  of  their  junction,  as  the  child 
chases  the  horizon,  only  to  discover  that  it  flies  as  we 
pursue  it.  There  is  thus  no  alternative,  but  either  to 
abandon  the  inquiry  after  an  immediate  intuition  of 
power,  or  to  seek  for  it  in  mind  as  determining  its  own 
modifications ; — a  course  open  to  those  who  admit  an 
immediate  consciousness  of  self,  and  to  them  only.     My 


28 


NATURE   OF 


first  and  only  presentation  of  power  or  causality  is  thus 
to  be  found  in  my  consciousness  of  myself  as  inllin^'^'' 

The  relation  subsisting  between  an  act  of  will  and  the 
motion  of  the  limbs,  or  between  a  physical  antecedent 
and  its  conseciuent,  he  regards  as  beyond  our  knowledge. 
*  Our  clearest  notion  of  efficiency  is  that  of  a  relation 
between  two  objects,  similar  to  that  which  exists  between 
ourselves  and  our  volitions.     But  what  relation  can  exist 
between  the  heat  of  fire  and  the  melting  of  wax,  similar 
to  that  between  a  conscious  mind  and  its  self-determina- 
tions ?      Or,  if  there  is  nothing   precisely  similar,   can 
there  be  anything  in  any  degree  analogous  ?     We  cannot 
say  that  there  is,   or,  if  there  is,  how  far  the  analogy 
extends,  and    how  and  where  it  fails.      We    can    form 
no  positive  conception  of  a  power  of  this  kind  :  we  can 
only   say,  that  it  is   something  different  from  the  only 
power  of  which  we  are  intuitively  conscious.     But,  on 
the  other  hand,  we  are  not  warranted  in  denying  the 
existence  of  anything  of  the  kind  ;  for  denial  is  as  much 
an  act  of  positive  thought  as  affirmation,  and  a  negative 
idea  furnishes  no  data  for  one  or  the  other  ^^' 

It  would,  however,  be  beside  my  purpose  to  enter  into 
a  detailed  account  of  the  history  of  this  controversy.  In 
consequence,  however,  of  its  historical  importance,  it 
seemed  essential  to  take  some  notice  of  it,  and  to  point 
out  that,  whatever  theory  may  be  adopted  as  to  the 
nature  of  Cause,  and  however  great  our  inability  to 
conceive  hmv  one  event  is  followed  by  another,  there  is, 

="  rrok^omena  Logica,  pp.  138,  139.  **  J  bid-  p-  M©. 


INDUCTIVE  INFERENCE. 


29 


at  least,  sufficient  definiteness  in  the  conception  to 
entitle  it  to  be  accepted  as  the  basis  of  scientific  reason- 
ing. \Mi ether  we  acknowledge  that  one  event  has 
invariably  the  poiver  of  producing  another,  or  whether 
we  content  ourselves  with  asserting  that  it  is  invariably 
followed  by  that  other,  it  is,  in  either  case,  the  element 
of  invarialf/eness  which  makes  the  connexion  or  con- 
junction, whichever  we  may  call  it,  a  fitting  object  of 
scientific  research.  But  remove  the  element  of  invari- 
ableness,  and  suppose,  if  it  be  supposable,  that  the  same 
antecedent  or  set  of  antecedents  is  sometimes  followed 
by  one  consequent,  and  sometimes  by  another,  and  some- 
times by  none  at  all ;  in  that  case  science  would  be 
impossible. 

The  student  who  wishes  to  obtain  further  information 
on  this  controversy  (a  controversy,  however,  which  pos- 
sesses a  historical  rather  than  a  practical  or  scientific 
interest)  is  referred  to  Hume's  Essay  on  the  Idea  of 
Necessary  Connexion  ;  Dugald  Stewart's  Dissertation^  Part 
II.  sect.  8 ;  Mill's  Logic^  Book  III.  ch.  v  ;  Sir  W.  Hamil- 
ton's Lectures  on  Metaphysics^  lectures  XXXIX,  XL ; 
Mansel's  Prolegome?ia  Logica,  ch.  v ;  Mill  on  Hamilton^ 
ch.  xvi ;  Lewes'  History  of  Philosophy^  Articles  on  Hume 
and  Kant.  I  refer  only  to  books  likely  to  be  within  the 
student's  reach.  In  quoting  or  referring  to  Hume,  I 
have  employed  only  his  Essays.  Many  writers  persist  in 
making  references  to  his  Treatise  of  Human  Nature^  a 
work  written  at  the  early  age  of  twenty-seven  and  after- 
wards repudiated  by  the  author  as  containing  an  imma- 


! 


30 


NATURE   OF 


ture  expression  of  his  opinions  ^^  In  the  Advertisement 
to  his  Essays,  he  desires  that  '  the  following  Pieces  may 
alone  be  regarded  as  containing  the  author's  philoso- 
phical sentiments  and  principles.' 

jYote  3.— That  a  cause  is ;  that  every 

event  has  a  cause  ;  that  the  same  cause  is  always  attended 
with  the  same  effect ;  are  obviously  three  distinct  pro- 
positions, and  still  there  are  few  writers  who,  in  their 
treatment  of  the  question  of  Causation,  have  not  more  or 
less  confounded  them.  The  first  proposition  (if  com- 
pleted) would  be  the  Definition  of  Cause,  the  predicate, 
of  course,  depending  on  the  view  adopted  with  reference 
to  the  question  discussed  in  the  previous  note.  The 
second  is  a  statement  of  the  Law  of  Universal  Causation, 
the  third  of  the  Law  of  the  Uniformity  of  Nature. 

It  will  be  observed  that  in  the  text  of  this  chapter  1 
have  said  of  each  of  these  laws  that  it  *  is  universally 
admitted  by  mankind,  or,  at  least,  by  the  reflecting 
portion  of  mankind.'  The  latter  clause  must  be  regarded 
as  emphatic,  and  suggests,  I  think,  a  sufficient  answer 
to  those  authors  who  call  in  question  their  universal 
reception.  Mr.  Lewes,  speaking  of  the  Law  of  Universal 
Causation,  says,  '  All  believe  irresistibly  in  particular 
acts  of  causation.     Few  believe  in  universal  causation  ; 

»  This  work  is  undoubtedly  of  the  highest  philosophical  interest, 
but  when  we  arc  concerned  in  determining  the  matured  philosophical 
opinions  of  Hume  it  cannot  be  regarded  as  authoritative.  It  is 
curious  to  find  a  recent  editor  of  Hume's  Essays  expressly  defending 
the  practice  on  which  I  have  animadverted  in  the  text.  See  Mr. 
Grose's  edition  of  Hume's  Essays,  vol.  i.  p.  39- 


INDUCTIVE  INFERENCE, 


3^ 


and  those  few  not  till  after  considerable  reflexion  '^'  He 
then  proceeds  to  adduce  the  case  of  a  student  of  chem- 
istr)',  who  could  not  be  convinced  of  the  truth  of  the 
l^w,  but  Mooked  upon  the  argument  as  an  unwarrant- 
able assumption.'  Now  I  venture  to  suggest  that  this 
incapacity  was  due  to  the  terms  of  the  proposition  not 
being  made  sufficiently  intelligible  to  him.  I  question 
whether  any  man  of  average  powers  of  understanding 
could  be  found  who  would  maintain  the  contradictory  of 
either  of  these  I^ws ;  who  would  assert,  that  is  to  say, 
that  an  event  might  happen  without  anything  to  account 
for  it,  or  that  a  repetition  of  exactly  the  same  circunv 
stances  might  be  followed  by  a  different  effect.  That  a 
considerable  amount  of  intelligence  is  necessary  in  order 
to  understand  the  general  terms  in  which  the  propositions 
are  stated,  is  undeniable,  but,  when  once  understood,  1 
presume  that  the  propositions  cannot  fail  to  be  ac- 
quiesced in.  Like  all  other  propositions,  however,  of 
wide  import,  they  may  be  both  understood  and  ac- 
quiesced in,  without  being  fully  realised.  It  is  the  full 
and  constant  realisation  of  these  Laws,  at  all  times  and 
under  all  circumstances,  which  mainly  distinguishes  the 
man  of  scientific  from  the  man  of  unscientific  habits  of 
thought.  The  unscientific  man  either  does  not  think  of 
enquiring  into  the  causes  of  the  phenomena  around  him, 
or  notes  with  little  precision  the  circumstances  which  he 
is  investigating.  The  scientific  man,  on  the  other  hand, 
insists  on  invariably  referring  the  phenomena  in  which 

**  Lewes'  History  of  Philosophy,  Article  on  Kant. 


3« 


NATURE   OF 


INDUCTIVE  INFERENCE. 


33 


he  is  interested  to  their  several  causes,  and  is  satisfied 
with  nothing  but  the  most  rigorous  enquiry  into  the 
relation  between  these  causes  and  their  effects. 

But,  it  may  be  asked,  if  the  I^ws  of  Universal  Causa- 
tion and  of  the  Uniformity  of  Nature  are,  on  reflexion, 
thus  universally  received,  by  what  mental  process  do 
men  assure  themselves  of  their  truth  ?  Of  the  origin  of 
these,  as  of  kindred  beliefs,  two  different  explanations 
are  offered  by  rival  schools  of  psychologists.  According 
to  one  school,  the  human  mind  is  so  constituted  that  it 
cannot  but  accept  them  ;  they  are  fundamental  beliefs 
which  exist  in  the  mind  prior  to  all  experience,  though 
it  is  experience  which  occasions  us  to  realise  our  pos- 
session of  them.  We  have  never  learnt  them  ;  we  have 
simply  discovered  that  we  possess  them.  Thus  Reid, 
speaking  of  our  conviction  that  the  future  will  resemble 
the  past^'  (what  we  now  call  the  Law  of  Uniformity 
of  Nature),  says,  *  The  wise  Author  of  our  nature  hath 

=*'  This,  however,  is  a  very  inadequate  statement  of  the  Law  of 
the  Uniformity  of  Nature.  '  It  has  been  well  pointed  out,'  says  Mr. 
Mill,  'that  Time,  in  its  modifications  of  past,  present,  and  future, 
has  no  concern  either  with  the  belief  itself,  or  with  the  grounds  of  it. 
We  believe  that  fire  will  burn  to-morrow,  l)ecause  it  burned  to-day 
and  yesterday  ;  but  we  believe,  on  precisely  the  same  grounds,  that 
it  burned  before  we  were  born,  and  that  it  burns  this  very  day 
in  Cochin  China.  It  is  not  from  the  past  to  the  future,  as  past 
and  future,  that  we  infer,  I  ut  from  the  known  to  the  unknown  ;  from 
facts  observed  to  facts  unobserved  ;  from  what  we  have  perceived, 
or  been  directly  conscious  of.  to  what  has  not  come  within  our 
experience.  In  this  last  predicament  is  the  whole  region  of  the 
future  ;  but  also  the  vastly  i^reater  portion  of  the  present  and  of  the 
past. -Mill's  Logic,  Bk.  HI.  ch.  iii. 


implanted  in  human  minds  an  original  principle  by  which 
we  believe  and  expect  the  continuance  of  the  course  of 
nature,  and  the  continuance  of  those  connexions  w^hich 
we  have  observed  in  time  past.  It  is  by  this  general 
principle  of  our  nature,  that,  when  two  things  have  been 
found  connected  in  time  past,  the  appearance  of  the  one 
produces  the  belief  of  the  other  ^l'  And  Dr.  Whewell, 
speaking  of  the  Law  of  Universal  Causation,  says,  *  We 
assert  that  "  Every  event  must  have  a  cause  " :  and  this 
proposition  we  know  to  be  true,  not  only  probably,  and 
generally,  and  as  far  as  we  can  see ;  but  we  cannot 
suppose  it  to  be  false  in  any  single  instance.  We  are  as 
certain  of  it  as  of  the  truths  of  arithmetic  or  geometry. 
We  cannot  doubt  that  it  must  apply  to  all  events  past 
and  future,  in  every  part  of  the  universe,  just  as  truly  as 
to  those  occurrences  which  we  have  ourselves  observed. 
What  causes  produce  what  effects ; — what  is  the  cause 
of  any  particular  event ; — w^hat  will  be  the  effect  of  any 
peculiar  process  ; — these  are  points  on  which  experience 
may  enlighten  us.  Observation  and  experience  may  be 
requisite,  to  enable  us  to  judge  respecting  such  matters. 
But  that  every  event  has  some  cause,  Experience  cannot 
prove  any  more  than  she  can  disprove.  She  can  add 
nothing  to  the  evidence  of  the  truth,  however  often  she 
may  exemplify  it.  This  doctrine,  then,  cannot  have  been 
acquired  by  her  teaching  ^\' 

32  Reid's   Inquiry  into  the  Human  Mind  on   the  Principles   of 
Common  Sense,  ch.  vi.  §  24. 

^  Whewell's  History  of  Scientific  Ideas,  Bk.  III.  ch.  ii.  §  i. 


I 


34 


NATURE  OF 


The  opposite  school  of  psychologists  (of  which  Mr. 
Mill  and  Professor  Bain  may  be  taken  as  the  modern 
representatives)  maintains  that  there  is  nothing  in  these 
and  kindred  beliefs  which  compels  us  to  distinguish  them 
generically   from  other  truths,  but  that,  like  all   other 
truths,  they  are  the  result  of  Experience.      From   our 
earliest  years,  we  have  been  so  constantly  accustomed 
to  observe  one  change  preceded  by  another  change,  and 
the  same  antecedents  followed  by  the  same  consequents, 
as  well  as  to  find  our  own  experience  in  these  respects 
corroborated  by  that  of  others,  that,  on  reflexion,  we  all 
acquiesce,  and  cannot  but  acquiesce,  in  the  statements 
which  generalise  these  facts.     This,  it  is  held,  is  a  suffi- 
cient explanation  of  that  universality  and  necessity,  which, 
by  the  advocates  of  the  intuitional  theory,  described  in 
the  last  paragraph,  are  supposed  to  distinguish  the  *  fun- 
damental beliefs  of  the  human  mind '  or  *  the  principles 
of  common  sense,'  as  they  are  called  by  these  authors, 
from  all  other  truths.     The  beliefs  have  acquired  the 
character  of  universality  and  necessity,  not  because  they 
have  sprung  from  any  other  source  than  our  ordinary 
beliefs,  but  because  of  the  constancy  and  variety  of  the 
experience  from  which  they  are  gained.     *In  fact,  our 
whole  lives,'  says  James  Mill,  *  are  but  a  series  of  changes, 
that  is,  of  antecedents  and  consequents.     The  conjunc- 
tion, therefore,  is  incessant ;  and,  of  course,  the  union 
of  the  ideas  perfectly   inseparable.     We  can  no  more 
have  the  idea  of  an  event  without  having  the  ideas  of 
its  antecedents  and  its  consequents,  than  we  can  have 


INDUCTIVE  INFERENCE, 


ro 


the  idea  and  not  have  it  at  the  same  time  ".'  But  here 
occurs  a  difficulty.  If  the  Laws  of  Universal  Causation 
and  of  the  Uniformity  of  Nature  are  inferred  from  par- 
ticular facts  of  causation,  are  generalisations  from  ex- 
perience, or,  in  other  words,  inductions,  how  is  it  that 
they  are  made  the  grounds  of  all  other  inductions  ?  Is 
not  this  to  argue  in  a  circle  ?  The  answer  tc  this  diffi- 
culty is  that  the  Laws  in  question  are  the  result  of  an 
uniform  and  constant  experience,  co-extensive  not  with 
the  life  of  he  single  individual  w^ho  employs  them,  but 
with  the  entire  history  of  the  human  race ;  that,  con- 
sequently, when  we  adduce  them  as  the  grounds  on 
which  our  other  inductions  rest,  we  are  performing  the 
perfectly  legitimate  process  of  resolving  narrower  into 
wider  cases  of  experience.  The  argument,  in  short,  is 
this  :  the  inference  from  this  narrow  field  of  observation 
(the  particular  induction  which  we  happen  to  be  making) 
must  be  allowed  to  be  true,  unless  we  are  prepared  to 
deny  one  or  other  of  the  much  wider  generalisations 
which  constitute  the  Laws  of  Universal  Causation  and 
of  the  Uniformity  of  Nature.  To  recur  to  the  instance 
adduced  in  the  text,  the  proposition  that  bodies,  subject 
to  the  action  of  gravity  only,  fall  through  equal  vertical 
spaces  in  equal  times,  can  be  called  in  question  only  on 


'*  James  Mill's  Analysis  of  the  Phenomena  of  the  Human  Mind, 
ch.  xi.  The  position  maintained  by  James  Mill  is  that  these  beliefs 
owe  their  un'  »ersality  to  the  fact  of  their  being  inseparably  associated 
with  all  our  other  cognitions.  This  is  only  another  mode  of  stating 
the  theory  which  derives  them  from  experience. 

D  2 


3*5 


NATURE   OF 


peril  of  doubting  one  or  other  of  the  fundamental  laws  ; 
thus,  the  doubt  which  might  attach  to  it  is  shifted  to 
two   other  propositions   which  no  one  would  think  of 
questioning.     Or,  to  state  the  same  position  in  a  slightly 
different  form,  this  particular  instance  is  shown  to  be 
a  member  of  an  infinitely  long  series,  the  other  members 
of  which  have  been  examined  and  approved ;  as,  there- 
fore, it  differs  in  no  essential  respect  from  them,  it  claims 
to  be  admitted  also.     There  is,  indeed,  throughout  this 
argument  one  assumption  ;  as  the  rival  theory  assumed 
the  trustworthiness  of  what  it  styled  our  *  fundamental 
beliefs,'  so  this  assumes  the  validity  of  experience.     But, 
unless  we  make  one  or  other  of  these  assumptions,  we 
must  be  prepared  to  maintain  that  knowledge  is  alto- 
gether impossible  ^^ 

There  is  a  third  theory  of  the  origin  of  universal  be- 
liefs which  combines,  with  certain  modifications,  both 
the  others.  It  would  admit  that  all  beliefs  alike  are 
ultimately  derived  from  experience,  and  still  it  would 
freely  adopt  the  language  that  there  are  some  beliefs 
which   are    *  native   to   the   human   mind.'     The   word 

M  It  should  be  noted  that  Dr.  Mansel,  while  agreeing  in  the 
main,  as  he  usually  does,  with  the  intuitional  school,  in  respect  to 
the  origin  of  our  belief  in  the  Law  of  Universal  Causation,  refers  to 
experience  the  origin  of  our  belief  in  the  Uniformity  of  Nature. 
'  The  belief  in  the  uniformity  of  nature  is  not  a  necessary  truth, 
however  constantly  guaranteed  by  our  actual  experience.'  Manscl's 
Metaphysics,  Chapter  on  Necessary  Truths.  Cp.  Prolegomena 
Logica,  ch,  v.  Dr.  Manscl's  treatment  of  these  questions  is,  in  many 
respects,  peculiar  to  himself. 


INDUCTIVE  INFERENCE, 


^1 


'experience,'  as  ordinarily  employed  by  psychologists, 
includes  not  only  the  experience  of  the  individual,  but 
the  recorded  experience  of  mankind.  On  the  theory, 
however,  of  which  I  am  now  speaking,  it  has  a  still 
more  extended  meaning ;  it  includes  experience,  or,  to 
speak  more  strictly,  a  peculiar  aptitude  for  forming 
certain  experiences,  trans7nitted  by  hereditary  descent 
from  generation  to  generation.  While  some  ideas  occur 
only  to  particular  individuals  at  particular  times,  there 
are  others  which,  from  the  frequency  and  constancy 
with  which  they  are  obtruded  upon  the  minds  of  men 
at  all  times  and  under  all  circumstances,  become,  after 
an  accumulated  experience  of  many  generations,  coti- 
natiiral^  as  it  were,  to  the  human  mind.  We  assume 
them,  often  unconsciously,  in  our  special  perceptions, 
and  when  the  propositions,  which  embody  them,  are 
propounded  to  us,  we  find  it  impossible,  on  reflexion, 
to  doubt  their  truth.  It  is  by  personal  experience  of 
external  objects  and  their  relations  that  each  man  re- 
cognises them,  but  the  tendency  to  recognise  them  is 
transmitted,  like  the  physical  or  mental  peculiarities  of 
race,  from  preceding  generations,  and  is  anterior  to  any 
special  experience  whatever  on  the  part  of  the  individual. 
This  theory,  to  which  much  of  modern  speculation  ap- 
pears to  be  converging,  is  advocated  with  great  ability  in 
the  works  of  Mr.  Herbert  Spencer  ^^ 

The  student  who  wishes  for  further  information  on  the 
questions  discussed  in  this  Note  is  referred  to  Dugald 
^  See  especially  his  work  on  the  Principles  of  Psychology. 


38         NATURE  OF  INDUCTIVE  INFERENCE. 

Stewart's  Philosophy  of  the  Human  Mind,  Part  II.  ch.  v. 
§  2  ''"^  ('  Of  that  Permanence  or  Stability  in  the  order  of 
Nature  which   is  presupposed  in  our  Reasonings  con- 
cerning Contingent  Truths  ') ;  Reid's  Intellectual  Pouters, 
Essay  VI.  ch.  vi ;  Reid's  Active  Poivers,  Essay  I.  ch.  iv  ; 
Hamilton's  Supple ?ne?itary  Dissertations  to  Reid's  Works, 
Note  A,  §  3,  Note  Q ;   Hamilton's  Lectures  on   Meta- 
physics,  Lectures  XXXIX,  XL ;  James  Mill's  Analysis 
of  the  Pheiiomena  of  the  Hutnan  Mind,  ch.  xi ;  Mill's 
Logic,  Book  III.  chs.  iii-v,  xxi ;  Mansel's  Prolegomena 
Logica,  ch.  v ;  Mansel's  Metaphysics,  Section  on  Neces- 
sary Truths  ;  Mill  on  Hamilton,  ch.  xvi ;  Lewes'  History 
of  Philosophy,  Article  on  Kant ;  Bain's  Moral  and  Mental 
Science,   Book  II.    ch.  vi,   with  Appendix  B;    Herbert 
S^QncQx's  Principles  of  Psychology.     The  student,  in  em- 
ploying these  references,  must  be  careful  to  distinguish 
between  what  relates  to  the  Law  of  Universal  Causation 
(sometimes  called  the  Principle  of  Causality)  and  the 
Law  of  the  Uniformity  of  Nature.     The  two  Laws,  as 
already  noticed,  are  not  always  distinguished  with  suffi- 
cient care. 

3'  In  Sir  W.  Hamilton's  edition  of  Stewart's  Works,  the  corre- 
sponding reference  is  Part  II.  Subdivision  I.  ch.  ii.  section  4,  sub- 
section 2. 


CHAPTER  II. 


Of  Processes  subsidiary  to  Induction, 

OF  the  various  mental  processes  subsidiary  to  In- 
duction proper,  it  will  be  sufficient  for  our  purpose  to 
discuss  Observation  and  Experiment,  Classification  (in- 
cluding Nomenclature  and  Terminology),  and  Hypo- 
thesis. 

§1.    Of  Observation  and  Experi?nent, 

These  words  are  now  so  familiar,  that  they  hardly 
require  any  explanation.  To  observe  is  to  watch  with 
attention  phenomena  as  they  occur,  to  expert jne?it  (or,  to 
adopt  more  ordinary  language,  to  perfortn  an  experiment) 
is,  not  only  to  observe,  but  also  to  place  the  phenomena 
under  peculiarly  favourable  circumstances,  as  a  pre- 
liminary to  observation.  Thus,  every  experiment  implies 
an  observation,  but  it  also  implies  something  more.  In 
an  experiment,  I  arrange  or  create  the  circumstances 
under  which  I  wish  to  make  my  observation.  Thus,  if 
two  bodies  are  falling  to  the  ground,  and  I  attend  to  the 
phenomenon,  I  am  said  to  observe  it,  but,  if  I  place  the 
bodies  under  the  exhausted  receiver  of  an  air-pump,  or 
cause  them  to  be  dropped  under  any  special  circum- 
stances whatever,  I  may  be  said  not  only  to  make  an 
observation,  but  also  to  perform  an  experiment.     Bacon 


40     PROCESSES  SUBSIDIARY  TO  INDUCTION. 

has  not  inaptly  compared  experiment  with  the  torture  of 
witnesses  \  Mr.  Mill  distinguishes  between  the  two  pro- 
cesses, by  saying  that  in  observation  wi^find  our  instance 
in  nature,  in  experiment  we  make  it,  by  an  artificial  ar- 
rangement of  circumstances.  '  When,  as  in  astronomy, 
we  endeavour  to  ascertain  causes  by  simply  watching 
their  effects,  we  observe;  when,  as  in  our  laboratories,  we 
interfere  arbitrarily  with  the  causes  or  circumstances  of 
a  phenomenon,  we  are  said  to  experiment'^' 

As  Observation  often  involves  little  or  no  conscious 
effort,  while  Experiment  always  implies  an  artificial 
arrangement  of  circumstances,  it  might  be  expected  that 
the  general  employment  of  the  former  for  scientific  pur- 
poses would  long  precede  that  of  the  latter.  And  this 
supposition  is  confirmed  by  the  History  of  Science. 
Though  it  is  false  to  affirm  that  Experiment  was  never 
employed  by  the  Greeks  ^  its  general  neglect  was  cer- 
tainly one  cause  of  the  little  progress  made  by  them  in 
the  physical  sciences. 

In  the  attempt  to  ascertain  the  effect  of  a  given  cause, 
there  can  be  no  question  of  the  general  superiority  of 

^  '  Quemadmodum  enim  in  civilibus  ingenium  cujusque,  et  occultus 
animi  affectuumque  sensus,  melius  elicitur,  cum  quis  in  perturbatione 
ponitur,  quam  alias  :  simili  modo,  et  occulta  naturae  magis  se  produnt 
per  vexationes  artium,  quam  cum  cursu  suo  meant.*    Nov.  Org.^  Bk.  I. 

Aph.  xcviii. 

■^  Thomson  and  Tait's  Natural  Philosophy,  vol.  i.  §  369. 

'  For  a  refutation  of  this  popular  misconception,  see  Mr.  Lewes* 
work  on  Aristotle^  ch.  vi.  Mr.  Lewes,  however,  seems  to  me  not 
sufficiently  to  recognise  the  slight  extent  to  which  Experiment  was 
employed  in  ancient  as  compared  with  modern  times. 


OBSERVATION  AND  EXPERIMENT, 


41 


Experiment  over  Observation.  To  be  able  to  vary  the 
circumstances  as  we  choose,  to  produce  the  phenomenon 
under  investigation  in  the  precise  degree  which  is  most 
convenient  to  us,  and  as  frequently  as  we  wush,  to  com- 
bine it  with  other  phenomena  or  to  isolate  it  altogether, 
are  such  obvious  advantages  that  it  is  not  necessary  to 
insist  upon  them.  Without  the  aid  of  artificial  experi- 
ment, it  would  have  been  impossible,  for  instance,  to 
ascertain  the  laws  of  falling  bodies.  To  disprove  the  old 
theory  that  bodies  fall  in  times  inversely  proportional  to 
their  weights,  it  w^as  necessary  to  try  the  experiment ;  to 
be  able  to  affirm  with  certainty  that  all  bodies,  if  moving 
in  a  non-resisting  medium,  would  fall  to  the  earth  through 
equal  vertical  spaces  in  equal  times,  it  was  essential  to 
possess  the  means  of  removing  altogether  the  resisting 
medium  by  some  such  contrivance  as  that  of  the  air- 
pum.p.  In  some  of  the  sciences,  such  as  Chemistry,  the 
Sciences  of  Heat,  Light,  and  Electricity,  it  is  next  to 
impossible,  at  least  in  their  inductive  stage,  to  advance  a 
single  step  without  the  aid  of  Experiment.  No  amount 
of  mere  Observation  would  ever  have  enabled  us  to 
detect  the  chemical  elements  of  which  various  bodies  are 
composed,  or  to  ascertain  the  effects  of  these  elements 
in  their  pure  state.  Even  when  Observation  alone 
reveals  to  us  a  fact  of  nature.  Experiment  is  often 
necessary  in  order  to  give  precision  to  our  knowledge. 
That  the  metals  are  fusible,  and  that  some  are  fusible  at 
a  lower  temperature  than  others,  is  a  fact  which  we  can 
conceive  to  have  been  obtruded  upon  man's  observation, 


42     PROCESSES  SUBSIDIARY  TO  INDUCTWK 

but  the  precise  temperature  at  which  each  metal  begins 
to  change  the  solid  for  the  liquid  condition  could  be 
learned  only  by  artificial  experiment. 

But,  though,  in   ascertaining   the   effect   of  a   given 
cause,  Experiment  is  a  far  more  potent  instrument  than 
Observation,  the  latter  process  is  also  available,  and  is 
frequently  of  the  greatest  service.     Thus,  the  Science  of 
Medicine  equally  avails  itself,  for  this  purpose,  both  of 
observations  and  experiments.     The  scientific  physician 
will  not  only  try  the  effects  of  different  medicaments, 
different  modes  of  diet,  and  the  like,  but  he  will  also 
7vatch  the  effects  on  the  organic  system  of  various  occu- 
pations, habits,  and  pursuits.     In  some  cases  even,  as 
in  all  astronomical  and  many  physiological  phenomena, 
the  only  means  open  to  us  of  ascertaining  the  effect  of 
a  given  cause  is  Observation.     If  we  wish  to  ascertain 
the  various  phenomena  attendant  on  a  shower  of  meteors 
or  a  total  eclipse  of  the  sun,  we  must  wait  till  the  shower 
of  meteors  occurs  or  the  total  eclipse  takes  place.     If 
we  wish  to  learn  the  effects  of  the  lesion  of  a  particular 
part  of  the  nervous  system,  we  must  generally  wait  till 
an  instance  offers  itself ;  there  are  many  experiments  too 
dangerous  and  too  costly  to  be  made,  at  least  in  the  case 

of  man. 

While,  however,  both  Observation  and  Experiment  are 
available  in  ascertaining  the  effects  of  a  given  cause, 
in  the  reverse  process  of  ascertaining  the  cause  of  a 
given  effect  Observation  alone  is  open  to  us.  *We 
can  take  a  cause,'  says  Mr.  Mill,  *and  try  what  it  will 


OBSERVATION  AND  EXPERIMENT, 


43 


produce ;  but  we  cannot  take  an  effect,  and  try '  [that 
is,  experimentally]  *  what  it  will  be  produced  by.  We 
can  only  watch  till  we  see  it  produced,  or  are  enabled 
to  produce  it  by  accident.*  In  those  cases,  consequently, 
in  which  effects  alone  are  patent  to  us,  and  the  causes 
are  concealed  from  our  view,  we  are  compelled,  unless 
we  are  able  to  reverse  the  problem  in  the  manner  noticed 
in  the  next  paragraph,  to  have  recourse  to  Observation. 
A  new  disease  makes  its  appearance :  the  mode  of  its 
action,  and  the  conditions  favourable  or  unfavourable  to 
its  diffusion,  can  only  be  learned  by  a  careful  observation 
and  comparison  of  cases. 

It  should,  however,  be  noticed  that  the  problem  of 
finding  the  cause  of  a  given  effect  is,  in  practice,  as,  for 
instance,  in  many  cases  of  chemical  analysis,  often  re- 
versed, and  that,  by  setting  in  action  a  variety  of  causes, 
we  try  to  discover  whether  any  one  of  them  will  produce 
the  effect  in  question.  Experiment  is  thus  substituted 
for  Observation. 

It  will  readily  be  seen  that  those  Sciences  which  de- 
pend wholly  or  mainly  on  Observation  are,  as  inductive 
sciences,  at  a  great  disadvantage  compared  with  those 
in  which  it  is  possible  largely  to  employ  Experiment. 
Where  we  wish  to  ascertain  the  effect  of  a  given  cause, 
and  we  cannot  make  the  instances  for  ourselves,  the 
want  of  appropriate  and  definite  instances  will  often 
completely  bafile  us.  And,  though  the  cause  of  a  given 
effect  can  only  be  learned  by  Observation,  this  is  gene- 
rally an  enquiry  of  extreme  difficulty,  requiring  to  be 


44     PROCESSES  SUBSIDIARY  TO  INDUCTION. 

supplemented  by  experiment,  or  the  actual  production 
of  the  given  effect  by  the  supposed  cause,  before  we  can 
be  certain  that  it  has  been  conducted  with  the  required 
accuracy.  Thus,  mere  observation  of  the  electrical  phe- 
nomena which  we  witness  in  the  heavens  could  never 
have  given  us  the  Science  of  Electricity.  The  experi- 
ments which  we  may  conduct  in  an  hour  are  often 
worth  a  century  spent  in  observations. 

In  the  Science  of  Astronomy  this  defect  is  more  than 
compensated  by  the  extreme  simplicity  of  the  pheno- 
mena, the  heavenly  bodies  being  regarded  by  us,  not  in 
themselves,  but  only  in  their  mutual  relations.     Hence, 
we  are,  at  a  comparatively  early  stage,  enabled  to  apply 
the  Deductive  Method,  and  to  solve  the  problems  of 
Astronomy  by  mathematical  calculations.     But  in  the 
very  complex  Science  of  Physiology  this  resource  is  not 
open  to  us,  and  hence  the  backwardness  of  those  de- 
partments of  physiological  science  in  which  direct  ex- 
periment  is   not   available.     Any  animal   or  vegetable 
organism  is  so  complex,  the  data  are  so  numerous,  and 
bear   to  each  other   so  many   different  relations,   that, 
hitherto,   it   has   been  found   impracticable   to   subject 
physiology,  at  least  in  any  detail,  to  a  deductive  treat- 
ment.    In  social  and  political  speculations,  the  want  of 
experiment  is,  to  some  extent,  supplied  by  statistics.     A 
social   or  political   experiment   is   generally  as  imprac- 
ticable as  an  experiment  in  physiology,  and  the  danger 
with  which  it  is  attended  is  often  incomparably  greater. 
But  the  number  of  observations  open  to  us  in  these 


OBSERVATION  AND  EXPERIMENT, 


45 


enquiries  (as,  for  instance,  in  respect  to  crime,  educa- 
tion, trade,  taxation,  &c.)  is  often  very  large,  and,  by 
carefully  comparing  and  systematising  them,  we  may 
frequently  detect  some  relation  between  two  circum- 
stances which  enables  us,  with  great  probability,  to 
infer  that  one  has  something  to  do  with  the  production 
of  the  other.  I  am  here,  however,  trenching  on  the 
province  of  those  chapters  which  treat  more  peculiarly 
of  inductive  inference. 

The  following  Rules  may  be  luid  down  for  the  right 
conduct  of  Observations  and  Experiments  : — 

Rule  I.  They  must  be  precise.  It  is  often  of  the 
utmost  importance  to  notice  the  exact  time  at  which 
an  event  occurs,  the  length  of  its  duration,  the  position 
of  an  object  in  space,  its  relation  to  surrounding  objects, 
and  the  like.  We  are  all  acquainted  with  the  prime  im- 
portance of  precision  of  detail  in  legal  evidence ;  it  is  no 
less  indispensable  in  scientific  research.  For  the  purpose 
of  enabling  us  to  attain  this  object,  various  instruments 
and  methods  have  been  invented.  As  instances  of  these 
devices  may  be  given,  amongst  instruments,  the  tele- 
scope, the  microscope,  the  thermometer,  the  barometer, 
measures  of  various  kinds,  the  balance,  the  dial,  the 
clock,  the  watch,  the  chronometer,  the  vernier,  the 
goniometer,  the  galvanometer,  the  thermo-electric  pile ; 
amongst  methods,  the  decimal  system  of  notation,  frac- 
tions both  vulgar  and  decimal,  the  divisions  of  time, 
the  various  contrivances  for  the  measurement  of  space, 
the   method   of  double-weighing,  the  method  of  least 


46      PROCESSES  SUBSIDIARY  TO  INDUCTION. 

squares,  the  personal  equation  in  astronomical  obser- 
vations. To  these  instances  might  be  added  numerous 
others,  but  these  will  be  sufficient  to  show  the  great 
aid  derived  by  what  may  be  called  the  natural  methods 
of  observation  from  artificial  contrivances.  The  Ther- 
mometer and  the  Method  of  Double-Weighing  furnish 
such  striking  exemplifications  of  the  assistance  thus 
afforded,  that,  though  they  are  probably  familiar  to 
most  of  my  readers,  it  may  be  desirable  to  explain 
them,  one  as  an  example  of  an  instrument,  the  other 

of  a  method. 

The  Thermometer  (it  is  not  necessary  here  to  describe 
the  different  kinds  of  thermometers)  is  a  contrivance  for 
determining  the  degree  of  temperature,  irrespective  of 
the  mode  in  which  it  affects  individual  organisms.     As 
our   sensibility  varies   considerably  under   different  cir- 
cumstances, so  that  what  at  one  time  affects  us  with 
the  sensation  of  hot  will  at  another  affect  us  with  that 
of  cold,  the  sense  of  touch  cannot  be  depended  upon 
for  giving   us   accurate   measurements   of  temperature. 
But  the  fact  that,  while  the  pressure  remains  unaltered, 
an  augmentation  of  temperature,  with  certain  rare  ex- 
ceptions (to  be  noticed  hereafter),  expands  the  bodies 
subject  to  its  influence  furnishes  us  with  such  a  means 
of  measurement.     We  take  a  substance  which  notably 
exemplifies  the  power  of  heat   in  expansion,  such   as 
mercury,  alcohol,  or,  where   it   is   necessary  to  ensure 
great  precision,  atmospheric  air  carefully  prepared,  and, 
by  confining  it  within  a  tube   and  marking  off  a  scale 


OBSERVATION  AND   EXPERIMENT. 


47 


of  measurements  along  the  side,  we  are  enabled,  by 
noting  the  degree  of  expansion  of  the  substance  in  the 
tube,  to  estimate,  at  least  approximately,  the  degree  of 
temperature  in  the  atmosphere  or  any  other  body,  the 
conditions  of  which  we  are  investigating. 

The  method  of  Double- Weighing  is  peculiarly  simple 
and  ingenious.  It  is  a  contrivance  for  remedying  any 
possible  inequality  in  the  effective  arms  of  the  beam  of 
the  Balance.  The  body  to  be  weighed  is  placed  at  one 
end  of  a  balance,  and  is  exactly  balanced  by  another 
body  placed  at  the  other  end ;  the  first  body  is  then 
removed,  and  its  place  supplied  by  a  standard  weight 
or  weights,  till  these  exactly  balance  the  second  body ; 
we  are  thus,  on  the  principle  that  things  which  are 
equal  to  the  same  thing  are  equal  to  one  another,  as- 
sured of  the  precise  equivalence  in  weight  of  the  body 
to  be  weighed  and  the  standard  weight  or  weights,  pro- 
vided, of  course,  that  we  can  depend  on  the  instrument 
giving  the  same  results  in  successive  weighings. 

It  frequently  happens,  however,  that  a  single  observa- 
tion may  greatly  mislead  us.  I  may  be  in  a  district  at 
one  time,  and  find  the  air  very  temperate  and  agreeable  ; 
the  next  time  I  come,  it  may  be  peculiarly  hot,  or  chill, 
or  moist.  I  may  see  a  man,  at  the  first  shot,  hit  his 
mark ;  but,  at  the  subsequent  shots,  he  may  fire  very 
wide  of  it.  Hence  the  importance,  whenever  there  is 
any  liability  to  error,  of  taking  an  average  of  observations. 
If  a  sufficient  number  of  observations  be  taken,  there  is 
every  probability  that  an  error  in  one  direction  will  be 


48      PROCESSES  SUBSIDIARY  TO  INDUCTION. 

compensated  by  an  error  in  the  other,  and  that  an  aver- 
age, derived  from  all  the  observations,  will  approximate 
much  more  nearly  to  the  truth  than  any  single  observa- 
tion is  likely  to  do.  Thus,  if  I  wish  to  ascertain  the  true 
character  of  the  climate  at  any  particular  place,  the  ob- 
servations I  consult  must  extend  over  a  considerable 
number  of  years ;  if  I  wish  to  estimate  truly  the  skill 
of  the  marksman,  I  must  watch,  not  a  single  shot,  but 
many  successive  ones.  The  average,  it  is  true,  is  liable 
to  error,  but  any  single  observation  is  much  more  so. 
There  is  hardly  any  department  of  science,  depending 
upon  observation,  in  which,  if  it  be  our  object  to  obtain 
precision,  this  method  is  not  indispensable*. 

Rule  II.   But,  though  it  is  necessary  to  be  precise  in 
our  observations  and  experiments,  it  is  also  important, 
in  order  to  avoid  distraction  and  waste  of  time,  to  attend 
only  to  the  7naterial  circumstances  of  the  case  we  are  in- 
vestigating.   A  physician,  for  instance,  in  prescribing  for 
his  patient,  would  not  now  think  it  necessary  to  take  an 
observation   of  the   planets,   nor  would   a   chemist,   in 
gathering  herbs  for  his  decoctions,  think  it  of  any  con- 
sequence to  notice  the  phase  of  the  moon.     A  caution 
should,  however,  be  added.     Before  neglecting  any  cir- 
cumstance in  our  observations,  it  is  of  the  utmost  im- 

*  The  student  who  may  wish  for  further  information  in  connexion 
with  Rule  I.  is  referred  to  Dr.  Whewell's  Novum  Organon  Rcno- 
vatum,  Bk.  III.  ch.  ii.,  and  Ilerschel's  Discourse  on  the  Study  of 
Natural  Philosophy,  §  387-9.      On  the  importance  of  taking  an 
average  of  observations,  see  Herschel's  Discourse,  §  236-30. 


OBSERVATION  AND  EXPERIMENT, 


49 


portance  to  have  ascertained  beyond  doubt  that  it  is  not 
material  to  the  subject  of  our  enquiries  ^  To  neglect 
this  caution  would  be  a  violation  of  the  first  Rule. 

Rule  III.  The  circumstances  under  which  an  observa- 
tion or  experiment  is  made  should,  except  in  the  very 
simplest  cases,  be  varied  as  much  as  possible.  A  phy- 
sician, in  studying  the  character  of  a  disease,  will  note 
its  effects  on  persons  of  different  ages,  constitutions, 
habits  of  life,  and  the  like.  An  astronomical  observer 
will  not  be  content  with  a  single  observation  of  a  newly- 
discovered  comet,  but  will  note  the  phenomena  which 
attend  it  at  various  stages  in  its  passage  through  the 
heavens.  A  chemist  will  combine  a  newly-discovered 
element  with  the  various  other  elements,  and  will  try 
upon  it  the  effect  of  heat,  pressure,  &c.  It  is,  of  course, 
implied  that  some  discretion  will  be  employed  in  the 
application  of  this  Rule,  and  that  the  variation  of  cir- 
cumstances will  not  be  carried  beyond  the  point  at 
which  there  is  some  probability  of  its  adding  to  our 
knowledge. 

'  The  neophyte  in  science  requires  to  be  reminded  that  observa- 
tions which  might  at  first  be  supposed  to  be  immaterial  are  often 
afterwards  found  to  be  amongst  the  circumstances  most  material  to 
the  enquiry.  *  Could  anything '  (says  Dr.  Rolleston,  in  his  Address 
before  the  Medical  Association  in  1868)  'have  seemed  at  first  sight 
to  be  more  impertinent,  more  otiosely  curious  and  trifling,  than  to 
enquire  during  an  epidemic  of  cholera  what  was  the  nature  of  the 
subsoil  in  the  area  it  w.as  ravaging,  to  what  depth  it  was  porous,  and 
at  what  level  the  water  was,  and  had  been  previously,  standing  in 
it?  Yet,  as  I  think,  Von  Pettenkofer  has  at  last  fought  out  and  won 
his  battle  on  these  points.' 

£ 


50      PROCESSES  SUBSIDIARY  TO  INDUCTIOy, 

Rule  IV.  The  phenomenon  under  investigation  should 
if  possible  be  isolated  from  all  other  phenomena,  or,  at 
least,  from  all  those  which  are  likely  to  interfere  with  our 
study  of  it.  In  studying  the  effects  of  the  action  of 
gravity  upon  bodies,  it  was  necessary  to  exhaust  the 
atmosphere  and  to  withdraw  the  support,  and,  by  thus 
isolating  the  phenomenon,  to  enable  us  to  perceive  how 
bodies  behave  when  subject  to  the  action  of  gravity  only. 
A  physician,  in  trying  the  effects  of  a  new  drug,  will,  at 
first  at  least,  administer  it  alone,  and  not  in  combination 
with  other  drugs  which  might  augment  or  counteract  its 
influence  on  the  system  ^ 

A  beautiful  instance  of  the  isolation  of  a  phenomenon 
is  afforded  whenever  there  occurs  a  total  eclipse  of  the 
sun.  As,  on  these  occasions,  the  moon,  by  a  curious 
coincidence,  exactly  covers,  or  rather  more  than  covers, 
the  sun's  surface,  and  thus  intercepts  all  light  from  it,  we 
are  able  to  see  certain  rose-coloured  protuberances,  pro- 
jecting, as  it  were,  from  the  dark  edge  of  the  moon,  but, 
in  fact,  proceeding  from  the  sun.  The  real  nature  of 
these  '  red  flames '  was  long  a  matter  of  dispute,  but  it 
seems  now  to  be  conclusively  settled  that  they  are 
portions  of  an  atmosphere  of  incandescent  hydrogen  in 
which  the  sun  is  enveloped,  and  which  often  shoots  out 

«  By  observing  the  third  of  these  rules  we  usually  prepare  our 
instances  for  the  application  of  what  will  hereafter  be  explained  as 
the  Method  of  A|;reement,  and  by  observing  the  fourth  for  the 
application  of  what  will  hereafter  be  explained  as  the  Method  of 
Difference. 


OBSERVATION  AND  EXPERIMENT. 


51 


in  these  flames  to  distances  estimated,  on  one  or  two 
occasions,  at  no  less  than  300,000  miles  ^.  They  can 
now  be  seen,  whenever  the  sun  is  shining,  by  means  of 
the  spectroscope  ;  but  had  it  not  been  for  the  isolation 
of  the  phenomenon  thus  produced  by  the  intervention 
of  the  moon,  astronomers  w^ould  have  till  quite  recently 
been  ignorant  of  its  existence.  Here,  to  use  a  bold 
metaphor,  we  might  say  that  Nature  herself  performs  an 
experiment  for  us. 

When  it  is  impossible  entirely  to  isolate  a  phenomenon, 
it  is  sometimes  possible  so  far  to  diminish  the  action  of 
the  concomitant  circumstances  as  to  be  able  accurately 
or  approximately  to  calculate  what  would  be  the  effect, 
if  they  were  altogether  absent.  Thus,  we  can  never 
altogether  remove  the  influence  of  friction  on  a  moving 
body,  but  we  can  so  far  diminish  it  as  to  be  able  to  say 
what  the  effect  would  be  were  no  such  influence  at  work. 
We  cannot  altogether  eliminate  the  influence  of  extra- 
neous circumstances  on  a  patient  subject  to  medical 
regime,  but,  by  due  care,  we  may  minimise  the  excite- 
ment, fatigue,  ennui,  or  other  unfavourable  conditions 
which  might  interfere  with  our  treatment. 

The  circumstances  under  which  we  perform  our 
experiments  being  more  in  our  own  power  than  those 
under  which  we  conduct  our  observations,  it  is  obvious 
that  the  foregoing  rules,  and  especially  the  third  and 
fourth,  can  be  more  easily  observed  in  experiments  than 
in  observations. 

'  See  Young  on  the  Sun,  p.  202. 
E  2 


52     PROCESSES  SUBSIDIARY  TO  TA'DUCTIOr/, 

§  2.   On  Classification,  Nomenclature,  and  Terminology. 

(i)  Of  Classification. 
A  classification,  in  the  widest  sense  of  the  term,  is  a 
division,  or  a  series  of  divisions  and  subdivisions  ^     The 
process  of  classifying  our  own  thoughts  or  feelings,  or 
the  actions  of  ourselves  or  others,  or  the  external  objects 
which  surround  us,  is  one  of  the  most  constant  occupa- 
tions of  the  mind.     Thus,  we  are  perpetually  dividing 
outward  objects  into  those  which  are  useful  or  those 
which  are  useless  or  noxious  to  us  ;   those  which  are 
useful  into  such  as  are  within  and  such  as  are  beyond 
our  power  to  attain  ;  those  which  are  useful  and  which  it 
is  within  our  power  to  attain   into  such  as  are  to  be 
sought  at  once,  and  those  the  effort  to  appropriate  which 
may  be  more  advantageously  postponed, — each  of  these 
divisions  admitting  of  almost  infinite  subdivision.  In  fact, 
as  has  frequently  been  remarked,  every  attribution  of  a 
general  name  implies  an  act  of  division  or  classification. 
When  we  speak  of  a  horse,  we  are  dividing  all  objects 
into  those  which  are  horses  and  those  which  are  not. 
When  we  speak  of  a  bay  horse,  we  are  superadding  to 
this  division  the  subdivision  of  horses  into  bay  horses 
and  those  of  any  other  colour. 

But  the  process  of  Classification  of  which  I  am  about 
to  treat,  though  the  same  in  kind  with  that  which  we 
employ  in  the  affairs  of  ordinar>'  life,  is  of  a  much  more 
complex  and  systematic  character.  The  great  difference 
is  that,  whereas  in  the  affairs  of  ordinary  life  we  generally 
»  See  Deductive  Logic,  Part  11.  ch.  viii. 


CLASSIFICA  TION-, 


53 


classify  objects  with  reference  to  some  one  principle,  that 
principle  varying  according  to  the  particular  purpose  we 
happen  to  have  in  view  (thus  we  classify  horses  according 
to  their  colour,  their  breed,  their  strength,  &c.,  each 
classification  being  suggested  by  some  distinct  purpose), 
a  scientific  classification  must  take  account  of  all  the 
points  of  difference  which  are  in  any  way  likely  to  facili- 
tate the  scientific  investigation  of  the  group.  The  purport 
of  the  science  being  defined,  the  classification  must  be 
based,  not  on  one  or  two  characters,  selected  arbitrarily, 
but  on  the  entire  assemblage  of  characters  which  the 
science  investigates.  Thus,  if  Botany  be  defined  as  the 
science  which  investigates  the  organisation  (including 
under  that  term  the  form,  structure,  and  functions)  of 
plants,  a  botanical  classification,  in  order  to  be  strictly 
scientific,  must  not  omit  to  take  into  account  any  part 
of  that  organisation.  But  it  is  evident  that  such  a 
requirement  would  produce  endless  confusion,  unless  we 
could  discover  some  mode  of  subordinating  the  char- 
acters, so  as  to  make  the  more  important  points  of 
difference  the  basis  of  the  higher  divisions  in  the  series. 
Hence  we  see  already  that  a  scientific  classification  must 
be  guided  by  at  least  two  principles,  a  review  of  all  the  char- 
acters or  distinguishing  marks,  so  far  as  they  are  known 
and  so  far  as  they  fall  within  the  scope  of  the  science, 
and  a  subordination  of  these  characters  one  to  another. 
To  these  principles  others  will  subsequently  be  added. 

Before  proceeding  to  the  attempt  to  ascertain  induc- 
tively facts  of  co-existence  or  causation  amongst  a  vast 


54      PROCESSES  SUBSIDIARY  TO  INDUCTION. 

mass  of  phenomena,  it  is  often  highly  important,  if  not 
essential,  to  arrange  these  phenomena  in  groups,  as  well 
as  to  determine  the  order  in  which  these  groups  them- 
selves shall  be  arranged.  Hence  the  importance  of  laying 
down  correct  rules  for  Classification  in  a  System  of  In- 
ductive Logic.  It  is  exclusively  as  subsidiary  to  Induction 
that  I  shall  here  consider  the  subject  of  Classification  ^ 

A  scientific  Classification,  regarded  as  subsidiary  to 
Induction  employed  for  scientific  purposes,  may  be  de- 
fined as  A  Series  of  Divisions,  so  arranged  as  best  to 
facilitate  the  complete  and  separate  study  of  the  several 
groups  which  are  the  result  of  the  divisions,  as  well  as  of 

»  It  will  probably  occur  to  the  student  that  the  materials  for 
Classification  can  themselves  only  be  obtained  by  Induction.  And 
this  is  true.  All  Classification  implies  the  prior  employment  of  an 
Inductiot^r  Ennmerationem  Simplicem,  by  which  we  establish  the 
fact  of  the  co-inherence  of  certain  attributes.  But  these  '  inductions 
of  co-existence  '  (see  pp.  7-9)»  w^'c^  P'"^^^^'^^  ^"'^  classifications,  are 
altogether  of  a  different  order  from  the  'inductions  of  causation' 
which  it  is  the  ultimate  aim  of  science  to  establish,  and  to  which  I 
regard  Classification  as  mainly  subordinate.  I  say  '  mainly  subor- 
dinate,' for,  of  course,  there  is  no  doubt  that,  when,  by  means  of 
certain  •  inductions  of  co-existence,'  we  have  constituted  a  class,  we 
are  in  a  more  favourable  position  than  before  for  detecting  additional 
facts  of  co-existence  among  the  associated  phenomena. 

When,  from  a  wide  experience,  I  find  that  the  attributes  «,  h,  c, 
d  e  invariably  co-exist  in  the  same  objects,  I  generally  constitute 
these  objects  into  a  class,  and  designate  them  by  a  class-name.  The 
name  thus  serves  to  recall  the  fact  of  the  co-inherence  of  the  attri- 
butes,  and  I  am  far  more  likely,  than  if  I  had  never  made  the 
classification,  to  discover  the  co-existence  with  the  other  five  of 
some  sixth  attribute,  say/  or  to  be  able  to  trace  some  causal  con- 
nexion  between,  say,  a  and  b,  or  a,  b,  and  c. 


CLASSIFICA  TION. 


55 


the  entire  subject  under  investigation.  *  The  general  pro- 
blem of  classification,'  says  Mr.  Mill  '^  *  in  reference  to 
these  [namely,  scientific]  purposes  may  be  stated  as 
follows  :  To  provide  that  things  shall  be  thought  of  in 
such  groups,  and  those  groups  in  such  an  order,  as  will 
best  conduce  to  the  remembrance  and  to  the  ascertain- 
ment of  their  laws.' 

The  sciences  of  Botany  and  Zoology  are  rightly  re- 
garded as  furnishing  the  best  examples  of  Scientific  Clas- 
sification. The  excellence  of  the  classifications  which 
they  present  may  be  referred  to  two  reasons.  The  first 
is  the  extraordinary  multiplicity  of  the  different  kinds  of 
animals  and  plants  which  are  found  on  the  surface  of  the 
globe  :  this  fact  has,  from  the  earliest  times,  exercised 
man's  ingenuity  in  the  attempt  to  name  them  and  reduce 
them  to  order.  The  second  reason  may  be  found  in  the 
imperfection  of  these  sciences  in  their  present  condition  : 
the  difficulty  of  discovering  laws  of  succession,  or,  in 
other  words,  relations  of  cause  and  effect,  in  the  animal 
and  vegetable  kingdoms  has  naturally  led  scientific 
enquirers  to  concentrate  their  attention  on  the  far  easier 
task  of  describing  and  arranging  the  objects  themselves. 
Mineralogy,  though  its  classifications  are  less  systematic 
and  complete,  is  also,  in  the  present  state  of  the  science, 
mainly  occupied  in  attempting  the  work  of  classification. 

The  best  means,  perhaps,  of  making  the  student  ac- 
quainted with  the  nature  of  scientific  classification  is  to 
compare  the  method  of  tiatural  classification  (which  aims 
"  Mill's  Logic,  Bk.  IV.  ch.  vii.  §  i. 


56     PROCESSES  SUBSIDIARY  TO  INDUCTION. 

at  being  strictly  scientific)  with  that  of  artificial  classifica- 
tion (which,  so  far  as  it  is  artificial,  is  not  scientific), 
giving  illustrations  from  the  sciences  of  Botany  and 
Zoology.  An  examination  of  the  natural  system  will 
enable  us  to  lay  down  certain  rules  for  scientific  classi- 
fication, and  I  shall  conclude  with  such  remarks  as  may 
seem  necessary  in  order  to  preserve  the  student  from 
erroneous  impressions. 

A  natural  system  of  Classification  aims  at  classifying 
objects  according  to  the  whole  of  their  resemblances  and 
differences,  so  far  as  these  are  recognised  by  the  science 
in  whose  service  the  classification  is  made.    But  amongst 
these  resemblances  and  differences  some  are  found  to  be 
invariably  attended  by  a  number  of  others,  and  conse- 
quently these,  as  the  more  important,  are  selected  as  the 
characters  by  which  to  discriminate  the  higher  divisions 
of  the  series,  the  less  important  characters  being,  through- 
out the  whole  series,  subordinated  to  the  more  important. 
This  successive  subordination  of  characters  and  the  con- 
sequent coincidence  of  the  groups  formed  by  our  classi- 
fications with  what  appear  to  be  the  great  divisions  of 
nature  are  the  peculiarities  which  mainly  distinguish  a 
natural  system.     An  artificial  system,  on  the  other  hand, 
is  one  which  selects  arbitrarily  some  point  of  difference 
amongst  the  objects  to  be  classified,  and  then,  so  far  as 
possible,   makes  this   or  similar  points  the  basis  of  its 
classifications.      No  system,  however,   as  we  shall  see 
presently,  is  purely  artificial.   Though  of  little  use,  except 
as   a   preliminary   effort,   for   the   purposes  of  science, 


CLASSIFICA  TION. 


57 


an  artificial  system  possesses  one  great  advantage.  As 
it  bases  its  divisions,  where  possible,  on  some  one 
property,  and  that  generally  something  which  at  once 
strikes  the  eye  (one  of  the  earliest  of  the  modern  attempts 
to  classify  plants  took  for  its  basis  the  form  of  the 
corolla),  it  is  peculiarly  easy  of  application,  and  can  be 
much  more  readily  learnt  than  a  natural  system.  It  thus 
often  serves  the  purposes  of  a  key,  by  which  we  may 
easily  discover  the  place  of  a  group  in  a  natural  system. 
I  now  proceed  to  offer  illustrations. 

In  Botany,  the  most  celebrated  artificial  system  is  that 
known  as  the  Linnaean,  though  Linnaeus  also  did  much 
towards  the  establishment  of  a  natural  system.  In  this 
system,  which  was  a  great  advance  on  preceding  artifi- 
cial systems,  the  main  basis  of  classification  is  the 
number  of  stamens  and  pistils  which  are  to  be  found  in 
the  flowering  plant.  This  character  is,  however,  to  some 
extent  modified  by  other  considerations,  such  as  the 
relative  lengths  of  the  stamens,  the  shape  of  the  fruit,  &c. ; 
so  far  as  these  modifications  are  admitted,  the  Linnaean 
system  approaches  to  a  natural  system.  The  annexed 
Tables  (extracted  from  Balfour's  Manual  of  Botany  ^^) 
will  give  the  student  some  idea  of  the  manner  in  which 
the  Classes  (higher  divisions)  and  the  Orders  (divisions 
intermediate  between  the  Classes  and  (ienera)  are  con- 
stituted according  to  the  Linnaean  system.  It  should  be 
premised  that  the  stamens  are  the  male  organs,  and  the 
pistils  the  female  organs  of  a  plant. 


58      PROCESSES  SUBSIDIARY  TO  INDUCTION. 


Tabular  View  of  the  Classes  of  the  Linn^an  System. 

A.  Flowers  present,  or  evident  Stamens  and  Pistils  (Phanerogam la). 
I.  Stamens  and  Pistil  in  every  flower. 

1.  Stamens  free. 

a.  Stamens  of  equal  length,  or  not  differing  in  certain  pro- 

portions ; 

in  number  I  Class  I.  Monandria. 

2  II-  Diandria. 

__         3  III.  Triandria. 

_        ^ IV.  Tetrandria. 

E  V.  Pentandria. 

6  VI.  Hexandria. 

y  VII.  Heptandria. 

8  VIII.  Octandria. 

Q IX.  Enneandria. 

IQ  X.  Decandria. 

I2-IQ XI.  Dodccandria. 

20  )  inserted  on  Calyx—  XII.  Icosandria. 

or  more  i      on  Receptacle  ...  XIII.  Polyandria. 

b.  Stamens  of  different  lengths ; 

two  long  and  two  short    XIV.  Didynamia. 

four  long  and  two  short    XV.  Tetradynamia. 

2.  Stamens  united; 

by  Filaments  in  one  bundle  ...      XVI.  Monadelphia. 

in  two  bundles    XVII.  Diadelphia. 

in  more  than  two  bundles  XVIII.  Polyadelphia. 

by  Anthers(Compound  flowers)    XIX.  Syngencsia. 

with  Pistil  on  a  Column XX.  Gynandria. 

II.  Stamens  and  Pistil  in  different  flowers  ; 

on  the  same  Plant XXI.  Monoecia. 

on  different  Plants XXII.  Dicecia. 

III.  Stamens  and  Pistil  in  the  same  or  \ 

in  different  flowers  on   the  >   XXIII.  Polygamia. 
same  or  on  different  Plants    ) 

B.  Flowers  absent,  or  Stamens  and  Pistils  )    ^^^^    Cryptogamia. 
not  evident    i 


CLASSIFICA  TION. 


59 


The  Classes  are  sub-divided  into  Orders,  as  will  be 
seen  from  the  next  Table,  on  a  less  uniform  plan  than 
that  on  which  they  were  themselves  constituted. 
Tabular  View  of  the  Orders  of  the  Linn^an  System. 


Class  I.v 
II. 

III. 

IV. 
V. 

VI. 


Monog)'nia^* i  Free  Style. 

Digynia 2  Free  Styles. 

Trigynia     3         — 

Tetragynia 4         — 

Pentagynia     5         — 

Hexagynia 6         — 

VII.  vHeptagynia  7         — 

Vlll.fOctogynia 8         — 

IX.    Knneagynia  9         — 

X.    Decagynia 10         — 

XI.  1  Dodecagynia    12-19  — 

XII.  I  Polygynia 20  and  upwards. 

XIII./ 

iGymnospermia Fruit  formed  by  four  Achsenin. 
Angiospermia   Fruit,  a  two-celled  Capsule  with 
many  seeds. 

Siliculosa Fruit,  a  Silicula. 

Siliquosa  Fruit,  a  Siliqua. 

Triandria,  Decandria,  &c.  (number  of  Stamens),  as  in 
Classes. 

/Polygamia  yFqualis  Florets  all  hermaphrodite. 

Superflua Florets  of  the  disk  hermaphro- 
dite, those  of  the  ray  pistilli- 
ferous  and  fertile. 

Frustranea  ...  Florets  of  the  disk  hermaphro- 
dite, those  of  the  ray  neuter. 

Necessaria  ...  Florets  of  the  disk  staminiferous, 

those  of  the  ray  pistil  I  iferous. 

Segregata Each  floret    having  a  separate 

involucre. 

Monogamia  Anthers  united, flowers  compound, 

*^  It  must  not  be  supposed  that  all  the  Orders,  Monog}'nia,  &c., 
exist  in  each  of  the  first  thirteen  Classes.  When  an  Order  is  absent, 
the  next  Order  which  is  present  takes  its  place  in  the  numerical 
arrangement.  Thus,  if  the  Order  Trigynia  be  absent,  and  the  next 
Order  which  is  present  be  Tetragynia,  as  in  Class  IV,  this  latter  will 
rank  as  the  third  Order. 


XIX. 


6o     PROCESSES  SUBSIDIARY  TO   INDUCTION. 


Ji^")  Monandria,  Diandria,  &c.  (number  of  Stamens),  as  in  the 

XXILJ  ^^^^'^'• 

-Moncecia Hermaphrodite,     staminiferous 

I  and  pistilliferous  flowers  on  the 

XXIII.  J  same  plant. 

I  DicEcia on  two  plants. 

(Xrioecia     on  three  plants. 

/Fillces  Ferns. 

Musci    Mosses. 

„,^  J  Hepaticie  Liverworts. 

-^^^^*  jLichenes    Lichens. 

AU ^le Sea-weeds. 

^Fun<T^i    Mushrooms. 

*  Even  as  an  artificial  method,'  says  Professor  Balfour", 
*  this  system  has  many  imperfections.  If  plants  are  not 
in  full  flower,  with  all  the  stamens  and  styles  perfect,  it 
is  impossible  to  determine  their  class  and  order.  In 
many  instances,  the  different  flowers  on  the  same  plant 
vary  as  regards  the  number  of  the  stamens.  Again,  if 
carried  out  rigidly,  it  would  separate  in  many  instances 
the  species  of  the  same  genus ;  but,  as  Linnaeus  did  not 
wish  to  break  up  his  genera,  which  were  founded  on 
natural  affinities,  he  adopted  an  artifice  by  which  he  kept 
all  the  species  of  a  genus  together.  Thus,  if  in  a  genus 
nearly  all  the  species  had  both  stamens  and  pistils  in 
every  flower,  while  one  or  two  were  m.oncecious  or 
dioecious,  he  put  the  name  of  the  latter  in  italics,  in  the 
classes  and  orders  to  which  they  belonged  according  to 
his  method,  and  referred  the  student  to  the  proper  genus 
for  the  description.' 

The  species  of  the  Linnnean  system  coincide  with  those 
of  the  natural  system.     The  same  is  mostly  the  case  with 
"  Balfour's  Manual  of  Botany ,  §  718. 


CLASSIFICA  TION, 


61 


the  genera,  or  next  higher  divisions.  The  Linnaean 
system  is,  therefore,  far  from  being  purely  artificial.  In 
fact,  when  we  come  to  the  lower  groups  of  vegetables 
(genera  and  species),  we  are  compelled  to  discriminate 
them  one  from  another  by  a  multiplicity  of  characters, 
so  that  a  purely  artificial  system  of  botany  would  be 
impossible. 

The  framers  of  natural  systems  of  botany,  instead  of 
selecting  some  one  character,  such  as  the  number  of 
stamens  and  pistils,  as  the  basis  of  the  higher  divisions, 
attempt  to  discover  a  number  of  characters,  any  one  of 
which,  if  employed  as  the  instrument  of  division,  would 
give  the  same  results  as  any  of  the  others.  This  coin- 
cidence of  divisions  founded  on  various  characters  is  a 
proof  that  we  have  reached  some  real  distinction  in 
nature.  The  main  division  of  plants  into  cellular  and 
vascular,  or  acotyledonous  and  cotyledonous,  and  the 
sub-division  of  vascular  or  cotyledonous  plants  into 
monocotyledonous  and  dicotyledonous,  furnish  remark- 
able instances  of  such  a  coincidence,  and  may  conse- 
quently be  regarded  as  corresponding  with  grand  divisions 
in  nature  itself. 

*  In  taking  a  survey  of  the  Vegetable  Kingdom,  some 
plants  are  found  to  be  composed  of  cells  only,  and  are 
called  Cellular ;  while  others  consist  of  cells  and  vessels, 
especially  spiral  vessels,  and  are  denominated  Vascular. 
If  the  embryo  is  examined,  it  is  found  in  some  cases  to 
have  cotyledons  or  seed-lobes,  in  other  cases  to  want 
them  :    and   thus    some   plants  are  cotyledonous ^   others 


62      PROCESSES  SUBSIDIARY  TO  INDUCTION, 


acotyledonoiis ;  the  former  being  divisible  into  monocofyle- 
donous,  having  one  cotyledon,  and  dicotykdo?ious,  having 
two  [or  more]  cotyledons.  The  radicle,  or  young  root 
of  acotyledons,  is  heterorhizal,  that  of  monocotyledons  is 
endorhizal,  that  of  dicotyledons,  exorhizai.  When  the 
stems  are  taken  into  consideration,  it  is  seen  that  marked 
differences  occur  here  also,  acotyledons  being  acrogenous, 
monocotyledons  endogenous,  and  dicotyledons  exogenous. 
The  venation  of  leaves,  parallel,  reticulated,  or  forked, 
establishes  the  same  great  natural  divisions ;  and  similar 
results  are  obtained  from  a  consideration  of  the  flowers, 
monocotyledons  and  dicotyledons  being  phanerogamous 
and  acotyledons  cryptogatnous' 

*Thus,  the  following  grand  natural  divisions  are  ar- 
rived at : — 

S  Crvpto- 

1.  Cellular...  Acotylcdonous.       Heterorhizal.     Acrogenous.    j  gainous. 

IMonocotyledonous.  Endorliizal.    Endogenous.  )  Phanero-  ^ 

2.  Vascular.  j^^j^,^^ylgjQ,^y^^g^        Exorhizai.      Exogenous,    j  gamous^'.' 

Having  established  these  Primary  Divisions  of  the 
vegetable  kingdom,  the  botanist,  guiding  himself  as  far 
as  possible  by  the  same  principles  as  those  on  which  the 
primary  divisions  were  formed,  proceeds  to  divide  and 
sub-divide  till  at  last  he  arrives  at  species,  which  are 
usually  defined  to  be  collections  of  individuals  so  nearly 
resembling  each  other  that  they  may  be  supposed  to  be 
descended  from  a  common  stock.  Thus,  the  Class 
*  Dicotyledones  or   Exogenoe '  is  sub-divided  into  four 

"  V»;iMoyxx\  Manual  of  Botany,  §§  7^3>  724- 


CLASSIFICA  TION, 


63 


sub-classes,  one  of  which  is  the  *  Thalamiflorae,'  char- 
acterised as  having  *  calyx  and  corolla  present,  petals 
distinct  and  inserted  into  the  thalamus  or  receptacle, 
stamens  hypogynous.'  This  sub-class  is  divided  into  a 
number  of  orders  (sixty  in  Professor  Balfour's  Maftual), 
one  of  which  is  Hypericaceae,  the  Tutsan  or  St.  John's- 
wort  family,  thus  described  : — 

'  Sepals  4-5,  separate  or  united,  persistent,  usually  with  glandular 
dots,  unequal ;  aestivation  imbricated.  Petals  4-5,  oblique,  often 
with  black  dots,  aestivation  contorted.  Stamens  hypogynous,  in- 
definite in  number;  generally  polyadelphous,  very  rarely  10,  and 
monadelphous  or  distinct ;  filaments  filiform  :  anthers  bilocular, 
with  longitudinal  dehiscence ;  carpels  2-5,  united  round  a  central  or 
basal  placenta;  styles  the  same  number  as  the  carpels,  usually 
separate  ;  stigmas  capitate  or  simple.  Fruit  either  fleshy  or  cap- 
sular, multilocular,  and  multivalvular,  rarely  unilocular.  Seeds 
usually  indefinite  in  number,  minute,  anatropal,  usually  exalbu- 
minous  ;  embyro  usually  straight. — Herbaceous  plants,  shrubs,  or 
trees,  with  exstipulate  entire  leaves,  which  are  usually  opposite  and 
dotted.     Elowers  often  yellow.' 

In  this  order  there  are  fifteen  known  genera,  one  of 
which  is  the  Hypericum,  which  is  thus  described  in 
Irvine's  Handbook  of  British  Plants : — 

'Hypericum,  St.  John's-wort.  Herbaceous  plants  or  shrubs, 
with  opposite  simple,  entire  leaves,  which  are  usually  furnished 
with  pellucid  dots  (reservoirs  of  essential  oil).  Sepals  five,  free  or 
united  at  the  base,  ovate,  slightly  unequal,  permanent.  Petals  as 
many  as  the  sepals,  obtuse,  spreading.  Stamens  indefinite,  com- 
bined at  the  base  into  three  or  five  sets,  with  small  roundish  anthers. 
Ovary  with  three-five  cells  or  carpels  and  as  many  styles,  with 
simple  stigmas.  Fruit  capsular,  rarely  baccate,  three-five-celled, 
with  numerous  seeds.* 


64     PROCESSES  SUBSIDIARY  TO  INDUCTION. 

This  genus  is  divided  into  sub-genera  or  sections,  one 
of  which  is  thus  described  : — 

*  Stems  herbaceous.      Stamens  in   three  parcels   (triadelphous) . 
Styles  three.     Capsule  three-celled,  three- valved.' 

The  sub-genus  or  section  is  again  divided  into  sub- 
sections, one  of  which  is  characterised  as  having  '  stems 
round,  sepals  with  ciliary  glands.'  This  sub-section  con- 
tains amongst  its  species  the  well-known  Hypericum 
Pulchrum,  '  Elegant  St.  John's-wort,'  thus  described  :— 

*  Stems  erect,  bent  at  the  base,  round,  glabrous,  simple  or  branch- 
ing. Leaves  ovate,  clasping,  coriaceous,  smooth,  with  numerous 
translucent  dots.  Flowers  in  opposite  panicled  cymes.  Sepals 
obovate,  roundish,  loith  a  point,  ciliated,  tvith  nearly  sessile  glands, 
Petals  oblong,  ribbed,  with  black  sessile  glands  ^^' 

The  first  peculiarity  which  strikes  us  in  these  descrip- 
tions is  the  large  number  of  characters  which  is  employed 
ill  constituting  even  the  higher  divisions  of  the  series. 
Instead  of  describing  merely  the  number  and  distribution 
of  the  stamens,  as  in  the  Linnoean  system,  we  have,  even 
in  the  description  of  the  Order,  a  reference  to  almost 
every  part   of  the  plant.      We  next  notice  the  much 
greater  definiteness  which  the  characters  assume,  as  we 
descend  lower  in  the  series.     Thus,  to  take  the  sepals 
as  an  instance,  the  description  of  the  sub-class  simply 
informs  us  of  the  presence  of  a  calyx,  while  each  suc- 
cessive division  (except   the   sub-genus)  gives  us  more 
and  more  definite  information  as  to  the  number,  posi- 
tion, form,  &c.  of  the  sepals  which  constitute  the  calyx. 
15  See  Ir\'ine's  Handbook  of  British  Plants,  under  Order  CIII. 


CLASSIFICA  TION, 


^5 


Again,  we  observe  that,  in  the  lower  divisions,  the  stem, 
leaves,  sepals,  and  petals  are  the  characters  which  are 
brought  into  greatest  prominence,  whereas  the  stamens 
and  the  various  parts  of  the  pistil  (the  carpels,  styles, 
and  stigmas),  which  are  employed  in  the  higher  divisions, 
disappear  from  the  lower,  as  no  longer  affording  grounds 
of  difference.  Now  the  stamens  and  pistil,  inasmuch 
as  any  peculiarity  in  them  is  generally  accompanied  by 
a  larger  number  of  peculiarities  in  other  parts  of  the 
plant,  are  usually  of  far  more  importance  than  the  corolla 
(petals)  and  calyx  (sepals),  and  therefore  it  is  reasonable 
to  suppose  that  the  grounds  of  difference  furnished  by 
them  would  be  likely  to  be  exhausted  in  the  higher 
divisions.  At  the  same  time  we  see  that,  in  the  instance 
we  have  taken,  the  sepals  and  petals  furnish  grounds  of 
difference  at  a  very  early  stage  of  the  classification,  and 
consequently  that  even  the  less  important  characters 
are  often  used  concurrently  with  others  to  determine 
the  higher  divisions. 

In  Zoology,  the  advantage  of  a  natural  over  an  artificial 
classification  is  more  readily  recognised  than  in  Botany, 
the  structure  and  functions  of  animals  being  more  fa- 
miliar and  apparent  than  those  of  plants.  A  division  of 
animals,  for  instance,  which  adopted  the  number  of  limbs 
as  its  sole  distinguishing  character,  and  thus  brought 
together,  as  quadrupeds^  the  ox  and  the  frog,  would  be  so 
absurd  on  the  face  of  it,  as  to  be  rejected  at  once.  *  No 
arrangement  of  animals,'  says  Dr.  WhewelP",  'which,  in 
"  History  of  the  Inductive  Sciences ^  Bk.  XVI.  ch.  vii,. 

F 


66      PROCESSES  SUBSIDIARY  TO  INDUCTION. 

a  large  number  of  instances,  violated  strong  and  clear 
natural  affinities,  would  be  tolerated  because  it  answered 
the  purpose  of  enabling  us  easily  to  find  the  name  and 
place  of  the  animal  in  the  artificial  system.     Every  system 
of  Zoological  arrangement  may  be  supposed  to  aspire 
to  be  a  natural  system.'     He  then  proceeds  to  give  an 
instance  of  an  attempt  to  constitute  an  artificial  classifi- 
cation in  the  ichthyological  branch  of  Zoology.     '  Bloch, 
whose  ichthyological  labours  have  been  mentioned,  fol- 
lowed in  his  great  work  the  method  of  Linncneus '  (who 
devoted  much  of  his  attention  to  the  classification  of 
animals  as  well  as  of  plants).     '  But  towards  the  end  of 
his  life  he  had  prepared  a  general  system,  founded  upon 
one  single  numerical  principle— the  number  of  fins  ;  just 
as  the  sexual  system  of  Linnaeus  is  founded  upon  the 
number  of  stamina :  and  he  made  his  subdivisions  ac- 
cording  to  the  position  of  the  ventral  and  pectoral  fins  ; 
the  same  character  which  Linnc-eus  had  employed  for  his 
primary  division.     He  could  not  have  done  better,  says 
Cuvier,  if  his  object  had  been  to  turn  into  ridicule  all 
artificial  methods,  and   to   show  to  what  absurd  com- 
binations they  may  lead.' 

'By  the  natural  method;  says  M.  Milne  Edwards'^ 
(whose  remarks  on  Zoological  Classifications  and  the 
Primary  Divisions  and  Classes  of  the  Animal  Kingdom 

"  See  Milne  Edwards'  Zoologie  (in  the  Cotirs  Hhitntaire  (Thistoire 
naturellc),  septieme  edition,  §§  364,  3^5-  There  is  an  English 
translation  of  this  work  by  Dr.  R.  Knox.  I  have  followed  it,  except 
in  a  few  places  where  it  does  not  accurately  represent  the  original. 


CLASSIFICA  TION, 


6^ 


are  well  worthy  of  the  attention  of  all  students  of  induc- 
tive logic),  *  the  divisions  and  subdivisions  of  the  animal 
kingdom  are  founded  on  the  whole  of  the  characters 
furnished  by  each  animal,  arranged  according  to  their 
degree  of  respective  importance ;  thus,  in  know^'ng  the 
place  which  the  animal  occupies,  we  also  know  the  more 
remarkable  traits  of  its  organisation,  and  the  manner  in 
which  its  principal  functions  are  exercised. 

*The  rules  to  be  observed  in  arriving  at  a  natural 
classification  of  the  animal  kingdom  are  of  extreme  sim- 
plicity, but  often  there  is  much  difficulty  in  the  appli- 
cation. They  may  be  reduced  to  two,  for  the  object  of 
the  zoologist  in  establishing  such  a  classification  is, — 

*  I  St.  To  arrange  animals  in  natural  series,  according 
to  the  degree  of  their  respective  affinities, — that  is  to  say, 
to  distribute  them  in  such  a  manner  that  those  species 
which  most  nearly  resemble  each  other  may  occupy  the 
nearest  places,  while  the  distance  of  two  species  from 
each  other  may,  in  some  sort,  be  the  measure  of  their 
non-resemblance. 

*  2nd.  To  divide  and  subdivide  this  series  according 
to  the  principle  of  subordination  of  characters, — that 
is  to  say,  by  reason  of  the  importance  of  the  differences 
which  these  animals  present  amongst  them.' 

The  Primary  Divisions  of  the  animal  kingdom,  accord- 
ing to  the  natural  system,  are  four,  there  being  four  types 
of  structure  and  of  nervous  organisation,  to  which  animal 
life  conforms. 

*  These  four  principal  forms  may  be  understood  by  a 

F  2 


68      PROCESSES  SUBSIDIARY  TO  INDUCTIOA^ 

reference  to  four  well-known  animals— the  dog,  the  cray- 
fish or  lobster,  the  snail,  the  asterias  or  sea-star. 

'  In  order  that  the  zoological  classification  might  be 
a  faithful  representation  of  the  more  or  less  important 
modifications  introduced  into  the  structure  of  animals, 
it  was  necessary  to  distribute  these  beings  into  four 
principal  groups  or  divisions ;  and  this  is,  in  fact,  what 

Cuvier  did. 

*The  animal  kingdom  is  divided  into  vertebrate  animals, 
articulated  or  annulated  animals,  molluscs  and  zoophytes. 

»  The  fundamental  differences  distinguishing  these  four 
primary  divisions  depend  chiefly  on  the  mode  of  arrange- 
ment of  the  different  parts  of  the  body  and  on  the  con- 
formation of  the  nervous  system.     It  is  easy  to  under- 
stand the  importance  of  these  two  dominant  characters  : 
to  feci  and  to  move  is  the  especial  character  of  animal 
life,   and   these   two  functions   belong  to  the    nervous 
system.     It  might  readily,  then,  be  anticipated  that  the 
mode  of  conformation   of  this   system  would  exert   a 
powerful  influence  over  the  nature  of  animals,  and  would 
furnish  characters  of  primary  importance  in  classification. 
*  The  general  disposition  or  mode  of  reunion  of  the 
difl'erent  parts  of  the  body  exercises  an  equally  important 
influence,  as  modifying  the  locahsation  of  the  functions 
and  the  division  of  the  physiological  result  ^'.' 
Vertebrate  animals  are  thus  described  :— 

*The  vertebrate  animals  resemble  man  in  the  more  importart 
points  of  their  structure ;   almost  all  the  parts  of  their  bodies  are 

"  Milne  Edwards,  §§  372,  373. 


CLASSIFICATION, 


69 


in  pairs,  and  disposed  symmetrically  on  the  two  sides  of  a  medial 
longitudinal  plane  ;  their  nervous  system  is  highly  developed,  and 
is  composed  of  nerves  and  ganglions,  and  of  a  brain  and  spinal 
marrow.  To  these  characteristics  we  may  add  that  the  principal 
muscles  are  attached  to  an  internal  skeleton,  composed  of  separate 
pieces,  connected  together,  and  disposed  so  as  to  protect  the  more 
important  organs,  and  to  form  the  passive  instruments  of  loco- 
motion; that  the  more  important  part  of  this  skeleton  forms  a 
sheath  for  the  brain  and  spinal  marrow,  and  results  from  the 
reunion  of  annular  portions,  called  vertebrae ;  that  the  apparatus 
for  the  circulation  is  very  complete,  and  that  the  heart  offers  at 
least  two  distinct  reservoirs ;  that  the  blood  is  red ;  that  the  limbs 
are  almost  always  four  in  number,  and  never  more;  finally,  that 
there  exist  distinct  organs  lodged  in  the  head  for  sight,  hearing, 
smell,  and  taste  ^^.' 

The  Primary  Division  (embranchement)  *  Vertebrate 
Animals'  is  subdivided  into  the  five  classes,  Mammals, 
Birds,  Reptiles,  Batrachia,  Fishes,  of  which  Mammals  arc 
thus  described  : — 

*  Organs  of  lactation.  Hot  blood.  Circulation  complete,  and 
heart  with  four  cavities.  Pulmonary  respiration  simple.  Lobes 
of  the  cerebellum  reunited  by  an  annular  protuberance.  Lower 
jaw  articulated  directly  with  the  cranium.  The  body  generally 
covered  with  hairs.     Viviparous.* 

*  There  exist  considerable  differences  amongst  the 
mammalia,  and  these  modifications  of  structure  serve  as 
the  basis  for  the  division  of  the  class  into  groups  of  an 
inferior  rank,  called  orders.  Most  of  these  groups  are 
so  distinct  as  to  admit  of  no  doubt  in  respect  of  their 
limits  :  they  constitute,  in  fact,  natural  divisions  ;  but  in 
others  the  line  of  demarcation  is  by  no  means  so  distinct. 

"  Milne  Edwards,  §  374. 


ro      PROCESSES  SUBSIDIARY  TO  INDUCTION-. 


Thus  a  mammal  may  have  points  of  resemblance  so 
close  to  two  groups  as  to  render  it  almost  indifferent  to 
which  it  be  referred.  To  some  naturalists,  differences 
appear  important  which  are  disregarded  by  others,  and 
hence  a  want  of  agreement  on  the  subject  of  classification 
has  always  prevailed. 

*  The  method  followed  here  is  nearly  the  same  as  that 
proposed  by  Cuvier.  It  rests  mainly  on  the  differences 
mammals  show  in  respect  of  their  extremities  and  teeth, 
differences  which  always  imply  a  crowd  of  others  in 
habits,  structure,  and  even  intelligence. 

*  Keeping  in  view  the  ensemble  of  these  characters,  the 
class  mammalia  may  be  divided  into  two  groups,— the 
monodelphic  and  didelphic, 

*The  monodelphic  or  monodelphian  are  the  more 
numerous,  and  are  distinguished  chiefly  by  their  mode  of 
development.  At  birth  they  are  already  provided  with 
all  their  organs,  and  before  birth  they  derive  their 
nourishment  from  the  mother  by  means  of  a  pla- 
centa. Their  brain  is  more  perfect  than  the  didelphian, 
by  the  presence  of  a  corpus  callosum  uniting  the  two 
cerebral  hemispheres.  Finally,  the  walls  of  the  abdo- 
men have  no  osseous  supports  attached  to  the  margins 
of  the  pelvis,  as  we  find  in  the  second  great  class  of 
mammals.  The  mammals  thus  organised  have  been 
subdivided  into  two  groups, — namely,  ordinary  mam- 
mals and  pisciform  mammals. 

*  The  ordinary  mammals  are  organised  principally  to 
live  on  solid  ground  ;  the  skin  is  provided  with  hairs. 


CLASSIFICATION, 


71 


These  animals  are  further  subdivided  into  ten  orders : 
the  bimana,  quadrumana,  cheiroptera,  insectivora, 
rodentia,  edentata,  carnivora,  amphibia,  pachydermata, 
and  ruminantia.  The  first  eight  of  these  orders  have 
flexible  fingers  and  toes,  with  nails  covering  only  the 
dorsal  aspect  of  the  toe  or  finger,  and  comparatively 
small ;  hence  they  have  been  called  unguiculata :  the 
last  two, — namely  the  pachydermata  and  ruminantia, 
have  the  extremity  of  the  finger  and  toe  entirely  en- 
closed in  a  hoof;  they  are  thus  called  ungulata. 

*  The  order  bimana  includes  only  man  :  in  him  alone 
the  arms  are  destined  for  prehension,  the  limbs  for 
progression  and  support  in  the  erect  attitude.  Thus, 
his  natural  position  on  the  soil  is  unmistakeably  vertical. 
The  teeth  are  of  three  kinds,  and  have  their  edges  on 
the  same  plane  ;  they  are  frugivorous  :  finally,  the  bram 
is  more    perfect,  more  highly   developed,   than    in  any 

other  animal  -^' 

Here  the  Order  is  co-extensive  with  the  Species,  but 
usually  the  Order  is  divided  into  Genera,  and  each 
Genus  into  Species.  Thus,  the  Order  'Carnivora'  is 
divided  into  the  Genera  'cat,'  'hyxna/  'dog,'  'bear,'  &c. 
Again,  the  Genus  'dog'  comprises  the  dog  properly 
so  called,  the  wolf,  and  the  fox.  The  Genus  'cat'  com- 
prises not  only  the  cat  properly  so  called,  but  the  tiger, 
lion,  panther,  &c. 

It  may  be  as  well  to  add  an  account  of  the  characters 
which  distinguish  respectively  the  Order  '  Carnivora,'  the 

2"  Milne  Edwards,  §§  409-412. 


•2      PROCESSES  SUBSIDIARY  TO  INDUCTION', 


(^enus  *  Felis,'  and  the  Species  *  I.eo,'  in  order  to  serve 
as  an  example  or  illustration  of  the  manner  in  which 
these  several  degrees  in  the  scale  of  Classification  are 
usually  described  : — 

*  The  order  of  camivora  is  composed  of  ordinary  unguiculnted 
mammals ;  the  form  of  their  dentition  is  complete,  but  they  have 
no  opposing  thumb.  According  to  the  mode  of  life  of  these 
nnimals,  their  intestinal  canal  is  short ;  their  jaws  and  their  muscles 
strong,  in  order  to  seize  and  devour  their  prey  ;  their  head  from  this 
circumstance  seems  large.  The  jaws  are  short,  thus  favouring  their 
strength,  and  the  form  of  the  temporal-maxillary  articulation  proves 
that  the  teeth  are  made  for  tearing  and  cutting,  not  for  grinding  or 
masticating.  The  canine  teeth  arc  large,  long,  and  very  powerful ; 
the  incisors,  six  in  number  in  each  jaw,  small ;  the  molars,  some- 
times adapted  merely  for  cutting,  in  others  surmounted  with  rounded 
tubercles,  presenting  no  conical  points,  arranged  as  in  the  insectivora. 
( )ne  of  these  molar  teeth  is  usually  much  longer  and  more  cutting 
tlian  the  others,  and  has  therefore  been  called  the  carnivorous  molar 
tooth;  behind  these  (on  each  side)  are  one  or  two  molars,  almost 
flat,  and  between  the  carnivorous  molar  and  the  canine  a  variable 
number  of  false  molars.  The  food  of  the  animal,  whether  exclu- 
sively composed  of  flesh  or  mixed  with  other  matters,  may  be 
judged  of  by  the  varying  proportions  of  these  cutting  or  tuber- 
culated  molars. 

'  Animals  of  this  order  have  generally  the  toes  armed  with  claws 
adapted  to  hold  and  to  tear  their  prey  ;  usually  also  they  have  no 
collar-bones.' 

The  following  are  the  characteristics  of  the  genus 
'  Felis,'  and  of  the  species  *  Leo '  : — 

*  Their  jaws  are  short,  and  are  acted  on  by  muscles  of  extra- 
ordinary strength ;  their  retractile  nails,  concealed  between  the 
toes  in  a  state  of  repose  by  means  of  elastic  ligaments,  are  never 
blunted.  Their  toes  are  five  in  number  on  the  anterior  limbs, 
and  four  on  those  behind.     Their  hearing  is  exceedingly  fine,  and 


CLASSIFICA  TION, 


n 


the  Dest  developed  of  all  their  senses.  They  see  well  by  day  and 
night,  but  they  are  not  far-sighted ;  in  some  the  pupil  is  elongated 
vertically,  in  others  it  is  round.  They  make  great  use  of  the  organ 
of  smell';  they  consult  it  before  'eating,  and  often  when  anything 
disturbs  them.  Their  tongue  is  covered  with  horny  and  very  rough 
points.  Their  coat  is  in  general  soft  and  fine,  and  the  surface  of 
the  body  very  sensible  to  the  touch  ;  their  whiskers  especially  szem 
to  be  instruments  of  great  sensibility.  Though  of  prodigious  vigour, 
they  generally  do  not  attack  animals  openly,  but  employ  cunning 
and  artifice.  They  never  push  their  prey  to  flight,  but,  watching  by 
the  margins  of  rivers  and  pools  in  covert,  they  spring  at  once  on 

their  victim. 

*  At  the  head  of  this  genus  stands  the  lion,  measuring  frequently 
twelve  feet  in  length,  or  over  six  feet  to  the  setting  on  of  the  tail  ; 
about  three  feet  in  height,  and  characterised  by  the  square  head,  the 
tuft  of  hair  terminating  the  tail,  and  in  the  male  by  the  mane  which 
flows  from  the  head  and  neck  ^^* 

The  process  by  which  the  Zoologist  constitutes  the 
Primary  Divisions  of  animal  life,  and  then  descends  from 
these  to  the  Species,  is  distinguished  by  the  same  pecu- 
liarities as  those  which  we  remarked  in  reviewing  the 
natural  classifications  of  the  Botanist.  In  one  step  or 
other  of  the  classification  almost  every  known  charac- 
teristic of  a  species  will  be  found.  As  we  descend  the 
series,  the  characters  gain  in  definiteness  and,  as  a  rule, 
lose  in  importance.  Moreover,  even  in  the  higher  divi- 
sions of  the  series,  numerous  characters  are  used,  and 
those  not  always  of  great  apparent  importance.  Thus, 
that  '  the  body  is  generally  covered  with  hairs '  is  one 
of  the  characters  of  Mammalia. 

The  student  will  now  be  in  a  position  to  understand 

21  Milne  Edwards,  §  414. 


74      PROCESSES  SUBSIDIARY  TO  INDUCTION. 

the  rules  which  may  be  laid  down  for  the  right  conduct 
of  a  Natural  Classification. 

I.  Not  only  the  lower,  but  the  lygher  groups  of  the 
series  should  be  so  constituted  as  to  differ  from  one 
another  by  a  multitude  of  characters.  It  is  only  when, 
as  is  the  case  in  the  primary  divisions  of  Botany  and 
Zoology,  we  arrive  at  the  same  divisions  from  a  variety 
of  different  considerations,  that  we  can  feel  assured  that 
our  groups  really  correspond  with  distinctions  in  Nature. 
It  is  this  coincidence^  in  the  higher  groups  of  the  series, 
of  divisions  formed  on  different  principles,  that  distin- 
guishes a  Natural  from  an  Artificial  Classification. 

II.  The  more  important  characters  should  be  selected 
for  the  purpose  of  determining  the  higher  groups.  This 
is  called  the  principle  of  the  subordination  of  characters. 
But  how  are  we  to  determine  the  relative  importance  of 
characters  ?  *  We  must  consider  as  the  most  important 
attributes,'  says  Mr.  Mill"^,  Hhose  which  contribute  most, 
either  by  themselves  or  by  their  effects,  to  render  the 
things  like  one  another,  and  unlike  other  things  ;  which 
give  to  the  class  composed  of  them  the  most  marked 
individuality;  which  fill,  as  it  were,  the  largest  space  in 
their  existence,  and  would  most  impress  the  attention  of 
a  spectator  who  knew  all  their  properties  but  was  not 
specially  interested  in  any.'  This  account  is  perfectly 
true,  but  it  seems  to  be  hardly  sufliiciently  definite.  The 
following  criteria  may  be  proposed  for  the  purpose  of 
discriminating  between  the  more  and  the  less  important 

•♦«  Mill's  Logic,  Bk.  IV.  ch.  vii.  §  2. 


CLASSIFICA  TION 


75 


properties  of  natural  objects,  (i)  A  character  which  is 
found  to  furnish  an  invariable  index  to  the  possession  of 
certain  other  characters  is  *of  more  importance  than  a 
character  which  furnishes  no  such  index.  Thus,  the 
internal  structure  of  an  animal  is  of  more  importance 
than  its  size,  and  the  mode  of  fructification  of  a  plant 
than  the  colour  of  its  flowers.  (2)  Amongst  such  char- 
acters, a  character  is  regarded  as  of  more  or  less  impor- 
tance, according  as  it  accompanies  a  greater  or  smaller 
number  of  other  differences.  Thus,  in  the  classification 
of  animals,  the  characters  from  which  the  classes  ungui- 
culata  and  ungulata  are  so  called  are  of  more  importance 
than  the  form  of  the  teeth,  which  is  used  in  distinguishing 
the  orders.  For  the  same  reason,  the  mode  of  growth 
of  flowering  plants  (which  leads  to  the  distinction  of 
endogenous  and  exogenous  plants)  is  of  far  more  im- 
portance, as  a  character,  than  the  number  of  stamens  or 
pistils.  Hence,  in  constituting  the  higher  divisions  of  a 
series  we  must  look  for  those  characters  which  are 
accompanied  by  the  largest  number  of  differences. 

III.  The  classification  should  be  gradual,  proceeding 
by  a  series  of  divisions  and  subdivisions.  When  the 
group  to  be  classified  consists  of  an  enormous  number 
of  species,  as  in  the  case  of  animals  and  plants,  the 
necessity  of  observing  this  rule  is  obvious.  To  descend 
at  once  from  the  Primary  Divisions  to,  say.  Genera  and 
Species,  would  render  the  Classification  comparatively 
worthless.  The  object  of  a  classification  being  to  bring 
together  those  groups  which  resemble  each  other  and  to 


"J^      PROCESSES  SUBSIDIARY  TO  INDUCTIOA', 

separate  those  groups  which  differ  from  each  other,  we 
must  take  account  of  degrees  of  resemblance  and 
difference,  so  that,  as  a  rule,  the  number  of  gradations 
will  increase  with  the  number  of  groups  to  be  classified. 
IJoth  in  Botany  and  Zoology,  the  grand  divisions  which 
seem  now  to  be  universally  recognised  are  Primary 
Divisions  or  Sub-Kingdoms  (embranchements).  Classes, 
Orders,  Genera,  and  Species.  Between  these  divisions 
various  other  divisions  are  interpolated,  according  to  the 
seeming  requirements  of  each  particular  system,  and  often 
according  to  the  views  of  each  individual  author.  More- 
over, below  Species  are  often  reckoned  Varieties,  and  even 
Varieties  are  sometimes  sul)divided,  this  being  especially 
the  case  when  animals  have  become  domesticated  or 
plants  cultivated.  Taking  as  an  instance  the  Anthyllis 
Vulneraria  (Common  Lady's  Finger),  the  divisions  and 
subdivisions  of  a  natural  classification  may  be  illustrated 
thus-^:— 


I.  Primary  Div 
II.  Class 

Subclass 
III.  Order   . 
Suborder 
Tribe   . 
Subtribe 
IV'.  Ge.nus    . 

Subgenus  or 
V.  Species 
Variety 
Race    . 
Variation 


ISION 


Secti 


on 


Cotyledones. 

Dicotyledones. 

Calyciflorse. 

Leguminosa^. 

PapilionacetC. 

Lotex. 

(ienisteae. 

Anthyllis. 

Wilneraria. 

Vulneraria'^*. 

Dillenii. 

Horibus  coccineis. 

Foliis  hirsutissimis. 


^'  Yi2Mowx\  Mamial  of  Botany,  §  725. 

*'  It  is  not  uncommon  in  the  classificatory  sciences,  as   in   this 


CLASSIFICA  TION, 


11 


In  very  extensive  groups,  other  divisions  may  be  inter- 
polated ;  thus  a  subgenus  or  section  is  often  divided  into 
a  subsection.  On  the  other  hand,  many  of  these  divi- 
sions often  disappear ;  if  a  genus  consist  of  only  a  small 
number  of  species,  and  there  be  no  very  striking  points 
of  difference  amongst  them,  we  may  descend  at  once, 
without  any  intermediate  divisions,  from  the  Genus  to 
its  various  Species.  Sometimes,  even,  an  order  may 
contain  only  a  single  genus,  or  a  genus  a  single  species, 
in  which  case  the  two  may  be  regarded  as  coextensive. 
In  the  case  of  Man,  we  saw  that  we  descend  at  once 
from  the  Order  to  the  varieties,  the  Order  Bimana  being 
coextensive  with  the  genus  and  species  Homo,  so  that 
here  three  even  of  the  grand  divisions  are  coincident. 

IV.  The  groups  should  be  so  arranged,  that  those 
which  have  the  closest  affinities  may  be  brought  nearest 
to  each  other,  while  the  distance  of  one  group  from 
another  may  be  taken  as  a  measure  of  their  dissimilarity. 
The  observation  of  this  rule  would  result  in  what 
Mr.  Mill  calls  *  the  arrangement  of  the  natural  groups 
into  a  natural  series.'  For  the  purposes  of  subsequent 
induction,  it  is  plain  that  it  is  of  the  utmost  importance 
not  widely  to  dissever  groups  which  present  many  phe- 
nomena in  common,  or  which  we  even  suspect  may  do 
so.  The  object  aimed  at  by  this  rule  is,  to  a  great 
extent,  attained  by  the  observation  of  the  Subordination 

instance,  to  assign  the  same  name  to  a  higher  and  lower  division, 
the  lower  division  exhibiting  in  a  marked  manner  the  characters 
possessed  in  common  by  the  various  members  of  the  higher  division. 


78      PROCESSES  SUBSIDIARY  TO  INDUCTION, 

of  Characters  (Rule  2),  according  to  which,  the  higher 
the  place  of  the  division  in  the  series,  the  more  important 
is  the  collection  of  characters  which  serves  to  constitute 
it.  If  Rule  2  were  duly  observed,  it  would  be  impossible 
for  any  two  widely  dissimilar  groups  to  be  brought  into 
juxtaposition  in  the  lower  divisions  of  the  series.  Thus, 
the  ox  and  the  frog,  the  primrose  and  the  mushroom, 
would  in  any  natural  system  be  at  considerable  distances 
from  each  other.  But  it  is  not  sufficient  to  observe  the 
rule  of  the  Subordination  of  Characters.  The  arrange- 
ment of  the  cognate  groups  in  each  division  should  be 
such  that  at  the  head  of  the  series  may  come  those 
groups  which  are  most  like  the  groups  of  the  preceding 
division,  while  at  the  bottom  of  the  series  may  come 
those  groups  which  are  most  like  the  groups  of  the 
subsequent  division.  Thus,  suppose  that  we  have 
Orders  A,  B,  C,  of  which  B  resembles  A  more  than  C 
does,  and  that  A  is  subdivided  into  the  genera  a'  a"  a"' 
//  b"  c\  B  into  the  genera  w'  w"  ft  0  p'  p"  ;  C  into  the 
genera  x'  x''  /,  /',  y"\  z  (of  which  the  genera  repre- 
sented by  the  earlier  letters  of  the  alphabet  are  more 
akin  to  each  other  than  those  represented  by  the  later, 
and  conversely) :  in  our  arrangement  we  ought  to  place 
c  in  juxtaposition  with  ;;/'  w",  and/'/''  in  juxtaposition 
with  y  x'\  the  remaining  groups  being  arranged,  as 
above,  on  the  same  principle.  If  such  an  arrangement 
could  be  effected,  it  is  plain  that  those  groups  which 
presented  in  the  greatest  intensity  the  principal  pheno- 
mena of  the  class  of  objects  under  investigation  would 


CLASSIFICA  TION, 


79 


come  first  in  the  series,  and  that  those  which  presented 
them  in  the  least  intensity  would  come  last.  In  Zoology, 
for  instance,  those  groups  wouW  come  first  which  pre- 
sented in  the  greatest  intensity  the  principal  phenomena 
of  animal  life,  and  in  Botany  those  which  presented  in 
the  greatest  intensity  the  principal  phenomena  of  veget- 
able life.  It  is,  of  course,  seldom,  in  the  arrangement  of 
natural  objects,  that  we  are  able  to  draw  up  an  exact 
table  of  precedence  amongst  the  groups  of  any  division, 
])ut  we  are  often  able  to  say  that  this  or  that  group  or 
collection  of  groups  (a  or  a'  a"  ^'")  should  rank  first  in 
the  series,  or  that  it  should  rank  before  some  other  group 
or  collection  of  groups.  Thus,  no  zoologist  would 
hesitate  to  assign  to  man  (the  Order  Bimana)  the  highest 
place  in  any  classification  of  Mammalia,  while  he  would 
place  next  the  Order  Quadrumana,  and  in  this  Order  he 
would  select  apes,  and,  amongst  apes,  the  anthropoid 
apes,  to  be  brought  into  closest  juxtaposition  with  man. 

This  rule  is  obviously  of  most  difficult  application.  It 
points  out  an  ideal  to  be  aimed  at,  but  one  which  is 
never  likely  to  be  perfectly  realised.  So  many  are  the 
])roperties  to  be  taken  into  consideration  in  every  natural 
object,  that  it  is  often  impossible  to  say  that  this  object 
is,  on  the  w^hole,  more  like  another  than  that.  The 
groups  of  the  higher  divisions  may  often,  those  of  the 
lower  may  sometimes,  be  tabulated  in  some  order  of 
precedence ;  but  there  remains  a  large  number  of  cases 
to  which  the  rule  is  inapplicable,  or  to  which,  at  least,  it 
has  not  yet  been  successfully  applied.     This  is  especially 


8o      PROCESSES  SUBSIDIARY  TO  INDUCTION', 

the  case  in  Botany,  where,  though,  in  respect  of  com- 
plexity of  structure  and  perfection  of  organism,  Vascular 
plants  may  be  ranked  above  Cellular,  and  Dicotyledons 
above  Monocotyledons,  there  are  many  cases  among  the 
subdivisions^  especially  of  Monocotyledons  and  Dicoty- 
ledons, where  no  order  of  precedence  can  as  yet  be 
satisfactorily  established.  But,  even  if  the  rule  were  of 
universal  application,  and  if  we  were  perfectly  acquainted 
with  all  the  properties  of  bodies  and  their  relative  value, 
it  would  not  follow  that  we  could  establish  what  Dr. 
Whewell,  in  his  opposition  to  this  doctrine  of  Classifica- 
tion by  Series,  calls  *a  mere  linear  progression  in  nature.' 
There  might  still  be  many  Orders,  Genera,  or  Species, 
which,  to  use  a  familiar  expression,  we  should  be  obliged 
to  bracket.  '  It  would  surely  be  possible,'  says  Mr.  Mill""', 
'  to  arrange  ?i\\p/aces  (for  example)  in  the  order  of  their 
distance  from  the  North  Pole,  though  there  would  be 
not  merely  a  plurality,  but  a  whole  circle  of  places  at 
every  single  gradation  in  the  scale.' 

Remark  i.  A  natural  classification  is  supposed  to  be 
complete,  when  it  has  descended  as  low  as  species, — 
a  species  being  regarded  as  a  group  consisting  of  indi- 
viduals, all  of  which  have  descended  from  a  common 
stock.  Or,  if  the  process  be  reversed,  and  the  classifica- 
tion be  an  ascending  instead  of  a  descending  one,  species 
are  regarded  as  the  starting-point  of  the  naturalist,  and  it 
is  supposed  that  the  problem  before  him  is  to  group  them 

«  Bk.  IV.  ch.  viii.  §  i.  Note. 


CLASSIFICA  TION. 


8i 


under  higher  divisions.     But  a  species  may,  as  we  have 
seen,  be  divided  into  varieties,  sub  varieties,  &c.     Now, 
in  what  consists  the  difference  between  the  relation  of  a 
variety  to  a  species  and  the  relation  of  a  species  to  a 
genus  ?     To  this  question  a  very  large  section  of  natur- 
alists now  maintain  that  no  satisfactory  answer  can  be 
given.     If  it  be  said  that  varieties  of  the  same  species 
may  be  developed  in  the  course  of  time,  but  that  species 
themselves  must  be  regarded  as  distinct,  it  may  be  asked 
on  what  grounds  this  supposition  rests.     Different  vari- 
eties of  the  same  species  are  certainly  more  like  each 
other  than  different  species  of  the  same  genus,  just  as 
species  of  the  same  genus  have  more  resemblance  than 
genera  of  the   same  order,  or  members  of  any   lower 
division  than  members  of  any  higher  division ;  but,  given 
a  larger  amount  of  time,  is  there  more  difficulty  in  sup- 
posing a  common  stock  for  the  different  species  of  a 
genus  than  for  the  different  varieties  of  a  species  ?     This 
is  the  question  originated  with  so  much  ability  by  Mr. 
Darwin  in  his  work  on  the  Origin  of  Species.     His  own 
solution  of  the  question  is  well  known.    *  It  will  be  seen,' 
he  says  ^'',  '  that  I  look  at  the  term  species,  as  one  arbi- 
trarily  given  for  the  sake  of  convenience  to  a  set  of 
individuals  closely  resembling  each  other,  and  that  it 
does  not  essentially  differ  from  the  term  variety,  which 
is  given  to  less  distinct  and  more  fluctuating  forms.   The 
term  variety,  again,  in  comparison  with  mere  individual 
differences,    is   also  applied    arbitrarily,   and   for   mere 
^  Darwin's  Origin  of  Species,  ch.  ii. 
G 


82      PROCESSES  SUBSIDIARY  TO  INDUCTION. 

convenience'  sake.'  It  does  not  fall  within  my  province 
to  discuss  the  question  of  the  '  Origin  of  Species,'  but  it 
is  desirable  that  the  student  should  be  aware  that  the 
practice  of  naturalists  in  stopping  at  species,  as  if  they 
were  the  *  infimae  species '  of  the  old  logicians  below 
which  divisions  need  not  proceed,  is  far  from  being 
universally  accepted. 

Remark  2.  As  our  knowledge  of  the  external  world 
becomes  enlarged,  the  number  of  natural  groups,  recog- 
nised by  the  classificatory  sciences,  is  being  continually 
increased.  Botanists  and  zoologists  (especially  the  former) 
are  constantly  discovering  or  recognising  new  varieties, 
frequently  new  species,  and  occasionally,  even,  new  genera 
and  orders.  *  The  known  species  of  plants,'  says  Dr.  Whe- 
well ",  *  were  10,000  at  the  time  of  Linnaeus,  and  are  now 
[a.d.  1858]  probably  60,000.'    The  increase  in  the  num- 
ber of  recognised  varieties,  sub-varieties,  &c.,  is  even  still 
more  rapid.     One  common  effect  of  these  constant  dis- 
coveries and  recognitions  is  to  bridge  over  what  previously 
appeared  to  be  gaps  in  nature,  thus  illustrating  the  fact 
that  there  are  but  few  breaks  in  natural  phenomena,  that 
there  pervades  nature  a  I^w  of  Continuity,  according  to 
which  a  group  seldom  occurs  to  which  some  other  group 
may  not  be  found  very  closely  allied.    So  complete,  some- 
times,  is  this  continuity,  that  it  becomes  very  difficult 
to  distinguish  the  groups  by  any  fixed  characters.     Two 

2'  History  of  Scientijic  Ideas,  Bk.  VIII.  ch.  ii.  §  6.  Of  course,  since 
Dr.  WhewtU's  time,  the  number  has,  again,  been  constantly  on  the 
increase. 


CLASSIFICA  TION. 


83 


species  (say)  are  discriminated,  and  then  a  third  group 
is  found  which  partakes  of  the  character  of  each  of  the 
others.  This  is  constituted  ^  new  species,  and  then  a 
fourth  group  is  found  intermediate  between  this  and  the 
first,  and  so  on.  *  It  has  been  shown,'  says  Dr.  Car- 
penter, as  quoted  by  Sir  W.  Grove  ^'^j  *  that  a  very  wide 
range  of  variation  exists  among  Orbitolites,  not  merely 
as  regards  external  form,  but  also  as  to  plan  of  develop- 
ment j  and  not  merely  as  to  the  shape  and  aspect  of  the 
entire  organism,  but  also  with  respect  to  the  size  and 
configuration  of  its  component  parts.  It  would  have 
been  easy,  by  selecting  only  the  most  divergent  types 
from  amongst  the  whole  series  of  specimens  which  I 
have  examined,  to  prefer  an  apparently  substantial  claim 
on  behalf  of  these  to  be  accounted  as  so  many  distinct 
species.  But  after  having  classified  the  specimens  which 
could  be  arranged  around  these  types,  a  large  proportion 
would  yet  have  remained,  either  presenting  characters 
intermediate  between  those  of  two  or  more  of  them,  or 
actually  combining  those  characters  in  different  parts  of 
their  fabric  ;  thus  showing  that  no  lines  of  demarcation 
can  be  drawn  across  any  part  of  the  series  that  shall 
definitely  separate  it  into  any  number  of  groups,  each 
characterised  by  features  entirely  peculiar  to  itself.'  We 
certainly  find  in  nature  a  persistency  of  type,  which  is 
the  result  of  the  laws  of  hereditary  transmission  ;  if  there 
were  no  such  persistency,  the  attempt  to  group  natural 

^  Essay  on  Continuity,  printed  at  the  end  of  the  Fifth  Edition  of 
The  Correlation  0/ Physical  Forces,  pp.  326,  327. 

G  2 


84     PROCESSES  SUBSIDIARY  TO  INDUCTION. 

objects  would  be  fruitless  and  absurd.  But,  at  the  same 
time,  when  we  have  succeeded  in  establishing  groups, 
we  constantly  find  that  there  are  individual  members 
diverging  more  or  less  from  the  ordinary  type,  and 
forming  intermediate  links  between  proximate  classes. 
To  adopt  and  alter  a  metaphor  employed  by  Dr.  Whe- 
well,  natural  classes  may  be  regarded  as  the  forests  of 
neighbouring  hills,  the  hills  being  seldom  separated  by 
well-defined  valleys,  and  the  valleys  being  frequently 
interspersed  with  straggling  trees  or  clumps. 

Remark  3.  It  sometimes  happens  that  one  of  the 
characters  by  which  classes  or  groups  are  distinguished, 
one  from  another,  is  to  be  found,  not  invariably,  but  only 
usually  or  occasionally  in  the  members  of  the  group. 
Thus,  in  the  description  of  the  Order  Rosaceae,  we  find 
that  '  the  seeds  are  erect  or  inverted,  usually  exalbumin- 
ous.  .  .  .  Flowers  sometimes  unisexual.'  Such  indefinite 
descriptions  would  be  entirely  out  of  place  in  an  artificial 
classification,  but  in  a  natural  classification,  where  the 
entire  assemblage  of  the  characters  must  be  taken  into 
consideration,  a  character,  though  not  found  invariably, 
or  even  though  found  but  seldom,  may  still  be  valuable 
in  distinguishing  a  group. 

Remark  4.  The  most  important  characters  are  not 
always  those  by  which  a  group  is  most  easily  recognised. 
For  the  purpose  of  recognition,  some  external  and  pro- 
minent character  or  set  of  characters  is  generally  best 
adapted.  Thus,  if  we  wished  to  determine  whether  a 
plant   were   monocotyledonous   or   dicotyledonous,    our 


CLASSIFICA  TION, 


85 


easiest  course  would  be  to  examine  the  stem ;  if  the 
stem  were  endogenous,  we  should  know  that  the  plant 
was  a  monocotyledon,  if  exogenous,  that  the  plant  was 
a  dicotyledon.  A  single  character  is  often  sufficient  to 
determine  the  place  of  a  plant  or  animal  in  a  series, 
because  we  already  know  that  the  possession  of  this 
character  is  a  sign  of  the  possession  of  the  various 
other  characters  which  are  enumerated  in  the  description 
of  the  natural  class.  The  method  of  determining,  by 
means  of  one  or  a  few  characters,  the  place  of  a  natural 
object  in  a  classification,  is  often  called  Diagnosis  or 
Characteristick.  *  The  Characteristick,'  says  Dr.  Whe- 
well-^,  'is  an  Artificial  Key  to  a  Natural  System.  As 
being  Artificial,  it  takes  as  few  characters  as  possible ; 
as  being  Natural,  its  characters  are  not  selected  by  any 
general  or  prescribed  rule,  but  follow  the  natural  affinities.' 
*  The  genera  Lamium  and  Galeopsis  (Dead  Nettle  and 
Hemp  Nettle)  are  each  formed  into  a  separate  group  in 
virtue  of  their  general  resemblances  and  differences,  and 
not  because  the  former  has  one  tooth  on  each  side  of 
the  lower  lip,  and  the  latter  a  notch  in  its  upper  lip, 
though  they  are  distinguished  by  these  marks.' 


Note. — Dr.  Whewell  maintains  that  natural  classes  are 
determined,  not  by  defitiitioti^  that  is,  by  an  enumeration 
of  characters,  but  by  type,  that  is,  by  resemblance,  more 
or  less  complete,  to  some  one  member  of  the  class,  round 
which  the  others  are  grouped.  Thus,  according  to  this 
^  History  of  Scientific  Ideas,  Bk.  VIII.  ch.  ii.  §  7. 


^6     PROCESSES  SUBSIDIARY  TO  INDUCTION-. 

theory,  the  Class  Mammah*a  would  be  determined,  not 
by  an  enumeration  of  characters,  but  by  resemblance, 
more  or  less  complete,  to  some  typical  specimen,  say 
Dog  ;  the  genus  Dog  would  be  determined  not  by  an 
enumeration  of  the  characters  which  are  common  to  the 
dog,  wolf,  and  fox  (the  species  comprised  in  the  genus), 
but  by  approximation  to  the  type-species  dog  :  similarly, 
the  Order  Rosaceae  would  be  determined  not  by  an 
enumeration  of  characters,  common  to  a  large  number 
of  genera,  but  by  the  resemblance,  more  or  less  complete, 
of  these  genera  to  the  type-genus  Rosa.  Dr.  WhewelFs 
view  will  be  understood  from  the  following  extract  :— 

*  In   a    Natural   Group the   class    is   steadily 

fixed,  though  not  precisely  limited ;  it  is  given,  though 
not  circumscribed ;  it  is  determined,  not  by  a  boundary 
line  without,  but  by  a  central  point  within ;  not  by  what 
it  strictly  excludes,  but  by  what  it  eminently  includes  ; 
by  an  example,  not  by  a  precept ;  in  short,  instead  of 
Definition  we  have  a  Type  for  our  director. 

*  A  Type  is  an  example  of  any  class,  for  instance,  a 
species  of  a  genus,  which  is  considered  as  eminently 
possessing  the  characters  of  the  class.  All  the  species 
which  have  a  greater  affinity  with  this  Type-species  than 
with  any  others,  form  the  genus,  and  are  ranged  about 
it,  deviating  from  it  in  various  directions  and  different 
degrees.  Thus  a  genus  may  consist  of  several  species, 
which  approach  very  near  the  type,  and  of  which  the 
claim  to  a  place  with  it  is  obvious ;  while  there  may  be 
other  species  which  straggle  further  from  this   central 


CLASSIFICA  TION, 


87 


knot,  and  which  yet  are  clearly  more  connected  with  it 
than  with  any  other.  And  even  if  there  should  be  some 
species  of  which  the  place  is  dlibious,  and  which  appear 
to  be  equally  bound  by  two  generic  types,  it  is  easily  seen 
that  this  would  not  destroy  the  reality  of  the  generic 
groups,  any  more  than  the  scattered  trees  of  the  inter- 
vening plain  prevent  our  speaking  intelligibly  of  the 
distinct  forests  of  two  separate  hills. 

'The  Type-species  of  every  genus,  the  Type-genus 
of  every  family,  is,  then,  one  which  possesses  all  the 
characters  and  properties  of  the  genus  in  a  marked  and 
prominent  manner.  The  Type  of  the  Rose  family  has 
alternate  stipulate  leaves,  wants  the  albumen,  has  the 
ovules  not  erect,  has  the  stigmata  simple,  and  besides 
these  features,  which  distinguish  it  from  the  exceptions 
or  varieties  of  its  class,  it  has  the  features  which  make  it 
prominent  in  its  class.  It  is  one  of  those  which  possess 
clearly  several  leading  attributes  ;  and  thus,  though  we 
cannot  say  of  any  one  genus  that  it  must  be  the  Type 
of  the  family,  or  of  any  one  species  that  it  viust  be  the 
Type  of  the  genus,  we  are  still  not  wholly  to  seek  :  the 
Type  must  be  connected  by  many  affinities  with  most 
of  the  others  of  its  group ;  it  must  be  near  the  centre 
of  the  crowd,  and  not  one  of  the  stragglers  •^^' 

'*  History  of  Scientific  Ideas ^  Bk.  VIII.  ch.  ii.  §  3.  art.  10.  Mr. 
Mill  {Logic,  Bk.  IV.  ch.  vii.  §§  3,  4)  examines  Dr.  Whewell's  views 
at  considerable  length.  He  appears  to  me,  in  this  examination,  to 
insist  too  em.phatically  on  what  he  calls  *  distinctions  of  kind,'  and 
to  assert,  without  sufficient  warrant,  that  *  the  species  of  Plants  are 
not  only  real  kinds,  but  are  probably,  all  of  them,  real  lowest  kinds, 


88      PROCESSES  SUBSIDIARY  TO  INDUCTION. 

There  is  much  force  in  what  Dr.  Whewell  here  says, 
but  his  main  position  appears  to  me  to  be  incorrect. 
May  not  the  various  steps  in  the  process  of  Classification 
be  described  as  follows?  We,  first,  observe  a  general 
resemblance  amongst  a  variety  of  groups.  Prompted  by 
the  observation  of  this  resemblance,  we  determine  to 
constitute  the  groups  into  a  distinct  class.  But  it  is 
not  sufficient  simply  to  enumerate  the  groups  which  the 
class  contains  ;  it  is  incumbent  upon  us  to  state  the 
principle  on  which  the  classification  is  made.  This 
statement  consists  in  an  enumeration  of  those  characters 
which  are  common  to  all  the  members  of  the  newly-con- 
stituted class,  and  which,  at  the  same  time,  distinguish 
them  from  the  members  of  other  classes,  with  the  addi- 
tion, in  some  cases,  of  certain  characters  which  belong 
to  most,  or  even  to  a  few  only,  of  the  members  of  the 
class.  Thus,  the  class  is  determined  (or  ^  given, ^  to  use 
Dr.  Whewell's  expression)  by  an  enumeration  of  char- 
acters. But,  when  the  class  is  once  familiar  to  us,  the 
repetition  of  the  class-name  suggests,  not  the  characters, 
but  some  typical  specimen  of  the  class,  some  one  group 
which  stands  out  prominently  as  possessing  the  characters 
by  which  the  class  was  determined ;  and  it  is  by  reference 
to  this  central  specimen,  as  it  were,  that  we  fix  the  posi- 
tion of  the  other  groups  and  adjudicate  on  the  claims  of 

Infimre  Species,  which  if  we  were  to  subdivide  into  subclasses,  the 
subdivision  would  necessarily  be  founded  on  definite  distinctions,  not 
pointing  (apart  from  what  may  be  known  of  their  causes  or  effects) 
to  any  difference  beyond  themselves.* 


NOMENCLA  TURE. 


89 


any  newly-discovered  group  to  take  its  place  by  the  side 
of  the  others.  Thus,  the  type-species,  type-genus,  or 
typical  order,  may  be  of  the  greatest  service  as  a  con- 
venient embodiment  of  the  characters,  but  the  characters 
must  be  enumerated,  and  the  class  determined,  before 
we  can  select  our  typical  example. 

(2)  Of  Nomenclature. 
Nomenclature  is  intimately  connected  with  Classifica- 
tion.     The   groups,  whether  natural   or   artificial,  into 
which  objects  are  distributed,  could  neither  be  recol- 
lected by  ourselves  nor  communicated  to  others,  unless 
they  were  fixed  by  the  imposition  of  names.     A  Nomen- 
clature is  a  collection  of  such  names,  applied    to   the 
members  of  the  various  divisions  and  subdivisions  which 
constitute  a  classification.   The  number  of  natural  groups, 
however,  is  so  enormously  large,  that  it  would  be  next  to 
impossible  to  devise,  and,  if  possible  to  devise,  it  would 
be   impossible   to   remember,  distinct  names  for  each 
group.     Thus,  the  known  species  of  plants,  for  instance, 
now  probably  far  exceeds  60,000,  and,  if  we  took  into  ac- 
count varieties,  sub-varieties,  &c.,  the  number  of  groups 
would  be  represented  by  many  multiples  of  this  sum. 
Some  artifice,  therefore,  is  necessary  by  which  a  com- 
paratively small   number   of  names   may  be   made   to 
distinguish   a   large   number   of  groups.      Botany   and 
Chemistry  furnish  admirable  examples  of  the  employ- 
ment of  such  an  artifice,  and  some  knowledge  of  the 
principles  which  guide  the  imposition  of  names  in  those 


90      PROCESSES  SUBSTDTARY  TO  INDUCTIO^T. 

two  sciences  (a  knowledge  which  may  be  easily  acquired) 
would  probably  be  of  more  service  to  the  student  than 
anything  which  he  might  learn  from  a  body  of  rules  for 
Nomenclature  in  general. 

In  Botany,  the  higher  groups  (including  genera)  have 
distinct  names.     Thus,  we  have  Dicotyledones,  Rosaceae, 
Rosa,  &c.     But,  when  we  arrive  at  the  species,  these  are 
known  by  the  generic  name  with  the  addition  of  some 
distinctive  attribute.     Thus,  the  genus  Geranium  is  re- 
presented in  the  British  Isles  by  thirteen  species,  called 
respectively  Geranium  phaeum,   G.   nodosum,  G.  sylva- 
ticum,  G.  pratense,  G.  sanguineum,  G.  pyrenaicum,  G. 
pusillum,    G.  dissectum,    G.   columbinum,    G.   rotundi- 
folium,   G.   moUe,   G.  lucidum,   G.  robertianum.      The 
specific  names  are  selected  from  various  considerations ; 
sometimes  in  honour   of  an  individual  (as   Equisetum 
Mackaii,  Rosa  Wilsoni),  sometimes  from  the  country  or 
the  district  in  which  the  plant  abounds,  sometimes  from 
the  soil  which  is  most  favourable  to  it,  sometimes  from 
some  peculiarity  in  the  plant  itself.     So  arbitrary  and 
fanciful  sometimes  are  these  names,  that  Linnaeus  (as 
we  are  told  by  Dr.  Whewell  '^^)  *  gave  the  name  of  Bau- 
hinia  to  a  plant  with  leaves  in  pairs,  because  the  Bauhins 
were  a  pair  of  brothers,  that  of  Banisteria  to  a  climbing 
plant,    in   honour   of    Banister,   who    travelled    among 
mountains.'      It  is  plain  that  a  name  which  describes 
some  peculiarity  in  the  plant  itself  is  of  most  service  to 
the  learner  ;   but  any  name,  easily  remembered,  serves 
'1  History  of  Scimtijic  Ideas,  Bk.  VIII.  ch.  ii.  §  6. 


NO  ME  NC LA  TURE. 


91 


the  main  purpose  of  a  nomenclature,  which  is  to  distin- 
guish one  group  from  another.  Varieties,  sub-varieties, 
&:c.,  are  distinguished  from  dich  other  on  the  same 
principle  as  species.  Thus,  as  we  have  seen,  of  the 
species  Anthyllis  Vulneraria  there  is  a  variety  Dillenii, 
and  of  the  variety  Anthyllis  Vulneraria  Dillenii  there 
is  a  '  race '  Floribus  coccineis,  and  of  the  race  there 
is  a  *  variation '  Foliis  hirsutissimis.  The  nomenclature 
of  Zoology  is  now  generally  constructed  on  the  same 
principle  as  that  of  Botany.  In  some  systems  of  Miner- 
alogy, three  names  are  employed,  namely,  those  of  the 
Order,  Genus,  and  Species,  as,  for  instance,  Rhombohe- 
dral  Calc  Haloide. 

The  nomenclature  of  Chemistry,  or,  at  least,  of  In- 
organic Chemistry,  which,  in  some  respects,  furnishes 
an  interesting  example  of  a  scientific  nomenclature,  is 
constructed  on  the  principle  of  making  the  prefixes  and 
affixes  of  the  words  employed  significant  of  the  nature 
of  the  substances  for  which  they  stand.  Thus,  we  have 
the  affixes  ide^  ic^  ous,  ate,  ite,  &c.,  and  the  prefixes  mono^ 
di\  fri,  sesqui,  &:c.,  each  having  a  special  significance, 
though,  unfortunately,  not  always  an  unambiguous  one. 

It  would  transcend  the  limits  of  this  work  to  give  an 
account,  sufficiently  clear  and  precise,  of  the  Nomen- 
clature of  Inorganic  Chemistry  (which,  moreover,  is  at 
present  in  a  transitional  state),  but  the  student,  who  is 
anxious  to  gain  some  idea  of  the  principles  on  which 
it  is  constructed,  can  refer  to  Watts'  Dictionary  of 
Chemistry^  vol.  iv.  art.  Nomenclature. 


92      PROCESSES  SUBSIDIARY  TO  INDUCTIOy, 

(3)  Of  Terminology. 

A  Nomenclature  of  a  Science  is,  as  we  have  seen, 
a  collection  of  names  of  groups.  A  Terminology  is  a 
collection  of  the  names  (or  terms)  which  distinguish  either 
the  properties  or  the  parts  of  the  individual  objects  which 
the  science  recognises.  Thus,  when  we  speak  of  the 
genus  '  Rosa,'  we  are  employing  the  nomenclature  of 
Botany ;  but,  when  we  say  that  the  individuals  of  the 
genus  'Rosa '  have  *  their  corolla  imbricated  before  flower- 
ing, their  styles  with  lateral  insertion,  their  carpels  nu- 
merous,' &c.,  we  are  employing  not  the  nomenclature, 
but  the  terminology,  of  the  science.  In  botany  we  have 
an  almost  perfect  example  of  a  complete  and  judiciously 
constructed  terminology. 

'  The  formation  of  an  exact  and  extensive  descriptive 
language  for  botany,'  says  Dr.  Whewell '-,  *  has  been 
executed  with  a  degree  of  skill  and  felicity,  which,  before 
it  was  attained,  could  hardly  have  been  dreamt  of  as 
attainable.  Every  part  of  a  plant  has  been  named  ;  and 
the  form  of  every  part,  even  the  most  minute,  has  had 
a  large  assemblage  of  descriptive  terms  appropriated  to  it, 
by  means  of  which  the  botanist  can  convey  and  receive 
knowledge  of  form  and  structure,  as  exactly  as  if  each 
minute  part  were  presented  to  him  vastly  magnified.  This 
acquisition  was  part  of  the  Linnaean  Reform.  "  Tourne- 
fort,"  says  Decandolle,  "  appears  to  have  been  the  first 
who  really  perceived  the  utility  of  fixing  the  sense  of  terms 

-2  History  of  Scicntijic  Ideas,  Bk.  VIII.  ch.  ii.  §  a. 


TERMINOLOGY. 


9.3 


in  such  a  way  as  always  to  employ  the  same  word  in  the 
same  sense,  and  always  to  express  the  same  idea  by  the 
same  word ;  but  it  was  Linnaeqs  who  really  created  and 
fixed  this  botanical  language,  and  this  is  his  fairest  claim 
to  glory,  for  by  this  fixation  of  language  he  has  shed 
clearness  and  precision  over  all  parts  of  the  science." 

*  It  is  not  necessary  here  to  give  any  detailed  account 
of  the  terms  of  botany.     The  fundamental  ones  have 
been  gradually  introduced,  as  the  parts  of  plants  were 
more  carefully  and  minutely  examined.    Thus  the  flower 
was  successively  distinguished  into  the  calyx,  the  corolla, 
the  stametis,  and  the  pistils :  the  sections  of  the  corolla 
were  termed  petals  by  Columna  ;  those  of  the  calyx  were 
called  sepals  by  Necker.     Sometimes  terms  of  greater 
generality  were  devised  ;  ^xs  perianth  to  include  the  calyx 
and  corolla,  whether  one  or  both  of  these  were  present  • 
pericarp  for  the  part  inclosing  the  grain,  of  whatever  kind 
it  be,  fruit,  nut,  pod,  &c.     And  it  may  easily  be  imagined 
that  descriptive  terms  may,  by  definition  and  combination, 
become  very  numerous  and  distinct.    Thus  leaves  may  be 
called  pinnatifid,  pi7inatipartite,  pi^inatisect,  pinnaiilobate, 
pahmitifid,  pabnatipartite,  &c.,  and  each  of  these  words 
designates  different  combinations  of  the  modes  and  extent 
of  the  divisions  of  the  leaf  with  the  divisions  of  its  outline. 
In  some  cases  arbitrary  numerical  relations  are  introduced 
into  the  definition  :  thus  a  leaf  is  called  bilobate  when  it 
is  divided  into  two  parts  by  a  notch ;  but,  if  the  notch 
go  to  the  middle  of  its  length,  it  is  bifid;  if  it  go  near  the 
base  of  the  leaf,  it  is  bipartite;  if  to  the  base,  it  is  bisect. 


94     PROCESSES  SUBSIDIARY  TO  INDUCTION', 

Thus,  too,  a  pod  of  a  cruciferous  plant  is  a  siliqua  if  it  be 
four  times  as  long  as  it  is  broad,  but  if  it  be  shorter  than 
this  it  is  a  silicula.  Such  terms  being  established,  the 
form  of  the  very  complex  leaf  or  frond  of  a  fern  is  exactly 
conveyed  by  the  following  phrase  :  "  fronds  rigid  pinnate, 
pinnae  recurved  subunilateral  pinnatifid,  the  segments 
linear  undivided  or  bifid  spinuloso-serrate."  * 

A  Terminology,  I  have  said,  comprises  the  terms 
appropriated  to  express,  not  only  the  parts  of  objects, 
but  also  their  properties.  Thus,  in  the  foregoing  ex- 
ample, the  words  *  sepals,'  '  petals,'  &c.,  express  parts  of 
the  plant,  the  words  *  pinnatifid,'  '  bilobate,'  &c.,  which 
are  applied  to  the  shape  of  the  leaves,  express  characters 
or  properties.  A  complete  terminology  must  be  so  con- 
structed as  to  express  every  shade  of  difference  in  all 
those  properties  which  are  recognised  in  a  scientific 
treatment  of  the  object.  Thus,  if  colour  be  regarded  as 
of  importance  in  the  description  of  a  plant,  mineral,  &c., 
it  is  essential  that  there  shall  be  some  appropriate  term 
by  which  to  describe  every  shade  of  colour.  But  there 
are  few  terms  which,  from  their  mere  signification,  can 
call  up  any  precise  idea  in  the  mind.  Hence  it  is 
necessary  to  fix  by  convention  the  precise  meaning  of 
every  technical  term  employed  in  science.  Again,  to 
appropriate  the  words  of  Dr.  Whewell,  *  The  meaning 
of  technical  terms  can  be  fixed  in  the  first  instance 
only  by  convention,  and  can  be  made  intelligible  only 
by  presenting  to  the  senses  that  which  the  terms  are 
to  signify.      The   knowledge  of  a  colour  by  its  name 


TERMINOLOGY. 


95 


can  only  be  taught  through  the  eye.     No   description 
can  convey  to  a  hearer   what  we    mean  by  apple-green 
or  French  grey.     It  might,  perhaps,  be  supposed   that, 
in    the    first    example,  the  term  apple,  referring    to   so 
familiar   an   object,    sufficiently  suggests  the  colour  in- 
tended.    But   it   may  easily  be  seen   that  this   is   not 
true;  for  apples  are  of  many  different   hues  of  green, 
and  it  is  only  by  a  conventional  selection  that  we  can 
appropriate  the  term  to  one  special  shade.     When  this 
appropriation  is  once  made,  the  term  refers  to  the  sen- 
sation, and  not  to  the  parts  of  this  term ;  for  these  enter 
into  the  compound  merely  as  a  help  to  the  memory, 
whether  the  suggestion  be  a  natural  connexion   as   in 
"apple-green,"  or  a  casual   one  as   in  "French  grey." 
In  order  to  derive  due  advantage  from  technical  terms 
of  this  kind,  they  must  be  associated  immediately  with 
the  perception  to  which  they  belong ;  and  not  connected 
with  it  through  the  vague  usages  of  common  language. 
The  memory  must  retain  the  sensation ;  and  the  tech- 
nical word  must  be  understood  as  directly  as  the  most 
familiar  word,  and  more  distinctly.     When  we  find  such 
terms  as  tin-white  ox  pinchbeck-brown,  the  metallic  colour 
so  denoted  ought  to  start  up  in  our  memory  without 
delay  or  search  'I'     When  we  have  fixed,  by  convention, 
the  meaning  of  a  term,  it  must  invariably  be  employed 
in  this   sense,  and  in  no  other.     The   least  vagueness 
or  inconsistency  in  the   use  of  terms   may  interpose  a 
fatal   obstacle  in  the  way,  not  only  of  the  learners,  but 
"  History  of  Scientifc  Ideas,  Bk.  VIII.  ch.  ii.  §  2. 


9^      PROCESSES  SUBSIDIARY  TO  INDUCTION', 

even  of  the  promoters  of  a  science.  The  progress  of  the 
Mechanical  Sciences  and  of  what  are  commonly  called 
Physics  was  long  retarded  by  the  vague  and  unintelligent 
use  of  such  words  as  *  heavy,' '  light/  *  hot,'  *  cold,'  *  moist,' 
*dry,'  &c.  Even  still  such  words  as  'force,'  *  fluid,' 
*  attraction,'  '  ether,'  &c.,  are  often  employed  without 
sufficient  precision. 

A  Terminology,  as  remarked  by  Dr.  Whewell  ^*,  is  in- 
dispensably requisite  in  giving  fixity  to  a  Nomenclature. 
Thus,  in  Botany,  '  the  recognition  of  the  kinds  of  plants 
must  depend  upon  the  exact  comparison  of  their  re- 
semblances and  differences ;  and,  to  become  a  part  of 
permanent  science,  this  comparison  must  be  recorded 
in  words.' 


Dr.  Whewell  devotes  the  last  Book  of  his  Novum 
Organon  Renovatum  to  a  series  of  aphorisms  on  the 
*  Language  of  Science,'  including  both  Nomenclature 
and  Terminology.  These  aphorisms  afford  one  of  the 
best  examples  of  Dr.  Whewell's  style  and  mode  of  treat- 
ment, and  will  well  repay  the  attention  of  the  student 
who  is  desirous  of  acquainting  himself  further  with  the 
methods  of  the  Classificatory  Sciences.  Mr.  Mill  has 
some  chapters  {Logic,  Bk.  IV.  chs.  iii-vi)  on  '  Naming ' 
and  the  '  Requisites  of  a  Philosophical  Language,'  and, 
in  addition  to  the  passage  already  referred  to,  Dr.  Whe- 
well treats  these  subjects  in  his  History  of  Scientific  Ideas, 
Bk.  L  ch.  ii;  Bk.  VIIL  ch.  ii.  §§  2  and  6  ;  Bk.  VIIL 

'*  Novum  Organon  Renovatum,  Bk.  IV.  Aphorism  ii. 


HYPOTHESIS, 


97 


ch.  iii.  art.  5.  In  Mr.  Bain's  Inductive  Logic,  there  is 
a  special  chapter  (Bk.  IV.  ch.  iii)  on  Classification,  and 
another  (Bk.  V.  ch.  vi)  on  the  Sciences  of  Classification. 

§  3.   On  Hypothesis. 

When  the  mind  has  before  it  a  number  of  observed 
facts,  it  is  almost  irresistibly  driven  to  frame  for  itself 
some  theory  as   to  the  mode  of  their   co-existence   or 
succession.     It  is  from  this  irresistible  impulse  to  refer  to 
some  law  the  various   phenomena  around    us    that    all 
science  as  well  as  all  scientific  error  has  sprung.   In  some 
cases,  as  we  have  seen    in  the  first  chapter^"',  a  single 
observation  or  experiment  may  at  once  establish  a  true 
theory  or  valid  induction,  independently  of  any  previous 
suppositions  on  our  part.     But,  in  all  the  more  intricate 
branches   of  enquiry,   true  theories    have    usually   been 
preceded   by  a  number   of  false  ones,  and  it  has   not 
unfrequently  occurred  that  the  false  theories  have  been 
mainly  instrumental  in  conducting  to  the  true.     Thus, 
the  elliptical  theory  of  planetary  motion  was  preceded  by 
the  circular  theory,  with  its  various  modifications,  and 
the   undulatory  theory  of  light  by  the  emission  theory. 
Rather  than  rest  satisfied  with  a  number  of  disconnected  * 
facts,  men  have  often  imagined  the  most  absurd  relations 
between  phenomena,  such  as  that  a  comet  was  the  har- 
binger of  war,  or  that  the  future  could  be  foretold  by 
birds.     These    theories,    assumptions,    or   suppositions, 
when  employed  provisionally  in  scientific  enquiry  and 

''  See  pp.  11,12. 
U 


98      PI^OCESSES  SUBSIDIARY  TO  INDUCTION. 

falling  short  of  ascertained  truths,  are  called  hypotheses^ 
and  have  already  been  alluded  to  in  the  first  chapter. 
The  word  '  hypothesis,'  as  commonly  employed,  is  ex-- 
elusive  of  propositions  which  rest  upon  absolute  proof, 
whether  inductive  or  deductive,  and  is  generally  used 
in  contradistinction  to  them.  Thus,  we  speak  of  a 
science  being  only  in  a  hypothetical  stage,  or  of  a 
hypothesis  being  converted  into  an  induction  or  being 
brought  deductively  under  some  general  law  already 
ascertained  to  be  true.  On  the  other  hand,  we  should 
hardly  dignify  with  the  name  of  'hypothesis '  a  supposition 
which,  at  least  in  the  eyes  of  its  framer,  did  not  possess 
some  amount  of  plausibility.  A  hypothesis  ^*  may  be  de- 
scribed as  a  supposition  made  without  evidence  or  without 
sufficient  evidence,  in  order  that  we  may  deduce  from  it 
conclusions  agreeing  with  actual  facts.  If  these  conclu- 
sions are  correctly  deduced,  and  really  agree  with  the  facts, 
a  presumption  arises  that  the  hypothesis  is  true.  More- 
over, if  the  hypothesis  relates  to  the  cause,  or  mode  of 
production  of  a  phenomenon,  it  will  serve,  if  admitted, 
to  explain  such  facts  as  are  found  capable  of  being  de- 
duced from  it.  And  this  explanation  is  the  purpose  of 
many,  if  not  most,  hypotheses.  Explanation,  in  the 
scientific  sense,  means  the  reduction  of  a  series  of  facts 
which  occur  uniformly  but  are  not  connected  by  any 
known  law  of  causation  into  a  series  which  is  so  con- 
nected, or  the  reduction  of  complex  laws  of  causation 

"'  The   following   sentences,   to  the   end  of  the  paragraph,  art 
slightly  altered  from  Mr.  Mill's  Log'u^  Bk.  III.  ch.  xiv.  §  4. 


HYPOTHESIS, 


99 


into  simpler  laws.  If  no  such  laws  of  causation  are 
known  to  exist,  we  may  suppose  or  imagine  a  law  that 
would  fulfil  the  requirement ;  and  this  supposed  \2i\\  would 
be  a  hypothesis. 

A  hypothesis  may  be  serviceable  in  many  ways.  In 
the  first  place,  it  may  afford  a  solution,  more  or  less 
probable,  of  a  problem  which  is  incapable  of  any  definite 
solution,  or  which,  at  least,  has  not  yet  been  definitely 
solved.  Thus,  many  of  the  advocates  of  the  Darwinian 
hypothesis  maintain  that  it  is  the  most  probable  solution 
of  an  insoluble  problem.  Secondly,  what  was  at  first 
started  as  a  hypothesis  may  ultimately  be  established  by 
positive  proof,  as  has  been  the  case  with  the  elliptical 
theory  of  planetary  motion,  and,  as  many  suppose,  with 
the  undulatory  theory  of  light.  Thirdly,  even  though 
a  hypothesis  may  ultimately  be  discovered  to  be  false,  it 
may  be  of  great  service  in  pointing  the  way  to  a  truer 
theory.  Thus,  as  already  remarked,  the  circular  theory 
of  planetary  motion,  and  the  supplementary  theory  of 
epicycles  and  eccentrics,  undoubtedly  contributed  to  the 
formation  of  the  hypothesis  which  was  eventually  proved 
to  be  true.  Kepler  himself  tried  no  less  than  nineteen 
different  hypotheses,  before  he  hit  upon  the  right  one,  and 
his  ultimate  success  was  doubtless  in  no  slight  degree 
due  to  his  unsuccessful  efforts.  There  is  hardly  any 
branch  of  science  in  which  it  might  not  be  affirmed 
that,  without  a  number  of  false  guesses,  true  theories 
could  never  have  been  attained.  Lastly,  a  hypothesis, 
whether   true    or    false,  if  it  be    applicable    to    all    the 

H  2 


ICO     PROCESSES  SUBSIDIARY  TO  INDUCTION, 

known  facts,  serves  as  a  means  of  binding  those  facts 
together,  of  colligating;  them,  to  use  a  technical  phrase, 
and  thus,  by  presenting  them  under  one  point  of 
view,  plainly  marks  off  the  phenomena  to  be  explained. 
A  theory,  like  the  Phlogistic  theory  in  Chemistry,  or 
the  theory  of  epicycles  and  eccentrics  (which,  by  being 
sufficiently  extended,  might  have  been  made  to  include 
all  the  phenomena  of  planetary  motion),  may  thus  have 
been  of  the  greatest  service  in  the  history  of  science, 
simply  by  keeping  before  the  minds  of  investigators  the 
precise  phenomena  which  demanded  an  explanation. 

The  formation  of  hypotheses  is  obviously  the  work  of 
the  imaginative  faculty,  a  faculty  of  hardly  less  importance 
in  science  than  in  art.  To  lay  down  rules  for  the  ex- 
ercise of  this  faculty  has  hitherto  been  found  futile.  The 
object  of  Inductive  Logic  is  rather  to  restrain  the  ex- 
uberant, than  to  excite  the  sluggish,  imagination.  The 
latter  office  is  best  fulfilled  by  recounting  the  great 
achievements  of  science,  and  thus  arousing  the  ambition 
and  kindling  the  enthusiasm  of  her  votaries.  The  former 
(which  is  no  less  necessary)  may  be  ])romoted  by  de- 
termining the  conditions  to  which  a  hypothesis  must 
conform,  in  order  that  it  may  rank  as  a  provisional 
explanation  of  facts,  and  before  it  is  entitled  to  demand 
the  honours  of  a  rigorous  inductive  examination.  These 
conditions  may  be  reduced  to  three  : — 

I.  The  hypothesis  must  not  be  known  or  suspected  to 
be  untrue,  that  is  to  say,  it  must  not  be  inconsistent  with 
facts  already  ascertained  or  the  inferences  to  which  they 


HYPOTHESIS. 


lOl 


lead^'.  It  w^ould  be  absurd,  for  instance,  in  the  present 
state  of  knowledge,  to  propose  design  or  compact  as 
the  cause  of  the  divergencos  which  are  found  in  the 
various  dialects  of  a  language,  or  to  suppose  the  heavenly 
bodies  to  move  in  perfect  circles.  So  simple  a  rule  as 
this  may  appear  to  be  superfluous,  but  it  seems  necessary 
to  include  it  in  the  conditions  to  which  a  hypothesis  must 
conform,  as,  otherwise,  a  perverted  ingenuity  might  suc- 
ceed in  framing  numberless  hypotheses  which  violated 
none  of  the  preliminary  conditions. 

II.  The  hypothesis  must  be  of  such  a  character  as 
to  admit  of  verification  or  disproof,  or  at  least  of  being 
rendered  more  or  less  probable,  by  subsequent  investiga- 
tions^^  Unless  this  restriction  were  placed  on  the  for- 
mation of  hypotheses,  there  would  be  no  limit  to  the 
wildness  of  conjecture  in  which  theorists  might  indulge. 

^"  The  explanation  of  this  nile,  contained  in  the  latter  clause  of 
the  sentence,  has  been  suggested  by  Mr.  Jevons'  chapter  on  the  Use 
of  Hypothesis,  a  chapter  which  may  be  read  with  advantage  by  the 
student.  His  second  condition  of  a  legitimate  hypothesis,  which 
corresponds  with  my  first,  is  expressed  thus  :  '  That  it  do  not  con- 
flict with  any  laws  of  nature,  or  of  mind,  which  we  hold  as  true.* 
Principles  of  Science,  vol.  ii.  p.  139, 

^^  It  may  occur  to  the  student  that  I  have  not  provided  for  the 
case  where  a  supposition  is  already  supported  by  a  certain  amount 
of  probable  evidence,  but  where  it  is  not  likely  to  be  rendered  more 
or  less  probable  by  further  investigation.  ]?ut  such  a  supposition, 
though  it  would  be  an  imperfect  induction  or  deduction,  could  hardly 
be  called  a  hypothesis,  a  term  which  seems  always  to  imply  some- 
thing provisional,  something  which,  on  further  enquiry,  may  be  either 
confirmed  or  weakened,  rendered  more  or  less  probable  than  it 
now  is. 


102     PROCESSES  SUBSIDIARY  TO  INDUCTIO.W 

It  might,  for  instance,  be  maintained  that  falling  bodies 
are  dragged  to  the  earth  by  the  action  of  invisible  spirits, 
and,  wild  as  such  a  theory  would  be,  there  is  nothing 
positively  to  disprove  it.  Granted  that,  like  many  other 
products  of  imagination,  such  a  theory  might  possibly 
be  true,  it  would  still  fall  without  the  scope  of  science. 
The  aim  of  science  is  proof,  present  or  prospective,  and 
consequently  what  neither  admits  of  proof,  nor,  so  far  as 
we  can  foresee,  is  ever  likely  to  admit  of  it,  or  even  of  ap- 
proximation to  it,  is  no  fitting  object  of  scientific  enquiry. 
As  affording  a  caution  against  the  unrestrained  exercise 
of  the  imagination  in  scientific  speculation,  it  may  be 
useful  to  adduce  a  few  instances  of  suppositions  or 
hypotheses,  which  were  probably  considered  as  perfectly 
satisfactory  by  those  who  proposed  them  or  amongst 
whom  they  were  prevalent,  which  would  now  be  regarded 
by  all  competent  authorities  as  absurd,  and  which  still  do 
not  admit  of  being  distinctly  disproved. 

It  was  once  very  generally  held  that  the  position 
of  the  planets  with  reference  to  the  earth  at  any  par- 
ticular moment  determines  not  only  the  course  of  human 
events  at  that  time,  but  the  subsequent  life  of  each 
person  born  under  the  '  conjuncture.'  Such  an  absurd 
theory  is  now  probably  held  by  no  single  person  of  sound 
understanding  ;  but,  so  complicated  is  the  web  both  of 
society  and  of  individual  life,  and  so  easy  would  it  be 
to  explain  '  apparent  exceptions  '  by  having  recourse  to 
*  counteracting  causes,'  that,  if  any  ingenious  person  were 
to  maintain  and  defend  this  theory,  it  would  probably 


HYPOTHESIS, 


103 


be  impossible  to  disprove  it.  Palmistry  affords  another 
instance  of  the  same  kind.  The  interlacing  of  the  lines 
on  the  palms  of  the  hands  is  said  to  indicate  a  man's 
*  fortunes.'  Such  a  notion  is  too  absurd  to  be  discussed  ; 
but,  if  maintained,  how  could  it  be  disproved  ?  It  might 
always  be  said  that  the  general  theory  of  palmistry  was 
true,  though  there  might  be  some  error  in  the  particular 
rules  by  which  the  *  fortune '  in  question  was  foretold  ^^ 

The  early  history  of  Geology  is  full  of  hypotheses  of 
this  kind.  The  following  examples  of  theories,  which 
no  scientific  man  would  now  entertain,  but  which  hardly 
admit  of  disproof,  are  extracted  from  Lyell's  Priticiples 
of  Geology  ^^ : — 

*  Andrea  Mattioli,  an  eminent  botanist,  the  illustrator  of 
Dioscorides,  embraced  the  notion  of  Agricola,  a  skilful 
German  miner,  that  a  certain  "materia  pinguis,"  or  "fatty 

""  The  superstitions  connected  with  dreams  afford  a  similar  in- 
stance: 'The  ancients  were  convinced  that  dreams  were  usually 
supernatural.  If  the  dream  was  verified,  this  was  plainly  a  prophecy. 
If  the  event  was  the  exact  opposite  of  what  the  dream  foreshadowed, 
the  latter  was  still  supernatural,  for  it  was  a  recognised  principle 
that  dreams  should  sometimes  be  interpreted  by  contraries.  If  the 
dream  bore  no  relation  to  subsequent  events  unless  it  were  trans- 
formed into  a  fantastic  allegory,  it  was  still  supernatural,  for  allegory 
was  one  of  the  most  ordinary  lorms  of  revelation.  If  no  ingenuity 
of  interpretation  could  find  a  prophetic  meaning  in  a  dream,  its 
supernatural  character  was  even  then  not  necessarily  destroyed,  for 
Homer  said  there  was  a  special  portal  through  which  deceptive 
visions  passed  into  the  mind,  and  the  Fathers  declared  that  it  was 
one  of  the  occupations  of  the  daemons  to  perplex  and  bewilder  us 
with  unmeaning  dreams.'— Lecky's  History  of  European  Morals^ 
vol.  i.  p.  385. 

*"  l-yell's  Princi pies  of  Geology,  ch.  iii. 


104     PROCESSES  SUBSIDIARY  TO  INDUCTION'. 

matter,"  set  into  fermentation  by  heat,  gave  birth  to  fossil 
organic  shapes.  Yet  Mattioli  had  come  to  the  conclusion, 
from  his  own  observations,  that  porous  bodies,  such  as  bones 
and  shells,  might  be  converted  into  stone,  as  being  permeable 
to  what  he  termed  the  *'  lapidifying  juice. '  In  like  manner, 
Falloppio  of  Padua  conceived  that  petrified  shells  were  gene- 
rated by  fermentation  in  the  spots  where  they  are  found,  or 
that  they  had  in  some  cases  acquired  their  form  from  "  the 
tumultuous  movements  of  terrestrial  exhalations."  Although 
celebrated  as  a  professor  of  anatomy,  he  taught  that  certain 
tusks  of  elephants,  dug  up  in  his  time  in  Apulia,  were  mere 
earthy  concretions ;  and,  consistently  with  these  principles, 
he  even  went  so  far  as  to  consider  it  probable  that  the  vases 
of  Monte  Testaceo  at  Rome  were  natural  impressions  stamped 
in  the  soil.  In  the  same  spirit,  Mercati,  who  published,  in 
1574,  fiiithful  figures  of  the  fossil  shells  preserved  by  Pope 
Sixtus  V.  in  the  Museum  of  the  Vatican,  expressed  an  opinion 
that  they  were  mere  stones,  which  had  assumed  their  peculiar 
configuration  from  the  influence  of  the  heavenly  bodies  :  and 
Olivi  of  Cremona,  who  described  the  fossil  remains  of  a  rich 
museum  at  Verona,  was  satisfied  with  considering  them  as 
mere  "  sports  of  nature."  Some  of  the  fanciful  notions  of 
those  times  were  deemed  less  unreasonable,  as  being  some- 
what in  harmony  with  the  Aristotelian  theory  of  spontaneous 
generation,  then  taught  in  all  the  schools.  For  men  who  had 
been  taught,  in  early  youth,  that  a  large  proportion  of  living 
animals  and  plants  was  formed  from  the  fortuitous  concourse 
of  atoms,  or  had  sprung  from  the  corruption  of  organic  matter, 
might  easily  persuade  themselves,  that  organic  shapes,  often 
imperfectly  preserved  in  the  interior  of  solid  rocks,  owed  their 
existence  to  causes  equally  obscure  and  mysterious.* 

*  As  to  the  nature  of  petrified  shells,  Quirini  conceived  that, 
as  earthy  particles  united  in  the  sea  to  form  the  shells  of 
mollusca,  the  same  cr)'stallizing  process  might  be  effected  on 
the  land ;    and  that,  in   the  latter  case,  the  germs  of  the 


HYPOTHESIS. 


IC^ 


I 


animals  might  have  been  disseminated  through  the  sub- 
stance of  the  rocks,  and  afterwards  developed  by  virtue  of 
humidity.  Visionary  as  was  this  doctrine,  it  gained  many 
proselytes  even  amongst  the  mdre  sober  reasoners  of  Italy 
and  Germany ;  for  it  conceded  that  the  position  of  fossil 
bodies  could  not  be  accounted  for  by  the  diluvial  theory.* 

It  has  been  maintained  by  theologians,  more  ardent 
than  discreet,  that  all  fossils  were  the  creations  of  the 
Devil,  whose  object  was  either  to  mimic  the  Almighty 
or  to  tempt  mankind  to  disbelieve  the  Mosaic  account 
of  the  creation.  Such  theories  admit  of  no  refutation  ; 
every  argument,  grounded  on  the  resemblance  of  fossil 
remains  to  living  organisms,  shows  only  more  distinctly, 
to  those  who  have  once  embraced  the  idea,  the  success 
of  the  alleged  agent  as  a  mimic  or  as  an  impostor. 

Other  instances  of  hypotheses  which  violate  this  rule  are 
afforded  by  the  Vortices  of  Descartes  and  the  Crystalline 
Spheres  of  the  ancient  astronomers,  both  of  which  were 
imagined  for  the  purpose  of  accounting  for  the  pheno- 
mena of  planetary  motion.  Both  of  these  hypotheses 
have  been  subsequently  disproved  by  the  free  passage 
of  comets  through  the  spaces  supposed  to  be  occupied, 
according  to  the  one  theory,  by  the  Vortices,  according 
to  the  other,  by  the  solid  Crystalline  Spheres.  But  at 
the  time  they  were  first  started,  there  was  no  reasonable 
ground  for  supposing  that,  if  untrue,  they  could  be  dis- 
proved, and,  what  is  more  important,  there  was  no 
possibility  of  proving  them  or  even  rendering  them 
more  probable ;  they  were  simply  freaks  of  imagination, 
incapable  of  proof  and,  to  all  appearance,  of  disproof. 


I06     PROCESSES  SUBSIDIARY  TO  INDUCTION. 

Another  theory  more  absurd  even  than  that  of  the  solid 
crystalline  spheres,  but  which  has  not,  like  that,  been 
positively  disproved,  is  the  curious  hypothesis  by  which 
Lodovico  delle  Colombe  endeavoured  to  reconcile  the 
Aristotelian  doctrine  that  the  moon  was  a  perfect  body 
with  the  recent  discoveries  of  Galileo,  who,  by  the  aid 
of  his  telescope,  had  found  that  its  surface  was  full  of 
hollows,  and  was  consequently  charged  by  his  enemies 
with  taking  a  fiendish  delight  in  distorting  the  fairest 
works  of  nature  ;  the  apparently  hollow  parts,  suggested 
Lodovico,  were  filled  with  a  pure  transparent  crystal,  and 
so  both  the  astronomer  and  the  Stagirite  were  right. 

It  will  be  observed  that  I  regard  hypotheses  as  ad- 
missible, even  though  they  are  not  likely  ever  to  be 
])ositively  proved  or  disproved,  provided  that  the  ac- 
cumulation of  further  evidence  is  likely  to  render  them 
more  or  less  probable.  Between  such  theories  and  the 
theories  just  exemplified,  which  are  neither  supported 
nor  likely  to  be  supported  by  any  evidence  whatever, 
there  is  the  widest  difference,  and,  while  the  one  have 
no  place  in  Science,  the  other,  I  conceive,  have  a  legi- 
timate claim  to  further  consideration.  The  ideal  of 
Science,  it  is  true,  is  proof;  but,  while  it  can  never 
recognise  mere  freaks  of  fancy,  it  is  often  compelled 
to  rest  content  with  probabilities.  Instances  of  hypo- 
theses such  as  I  have  in  view  are  the  Darwinian 
hypothesis  and  the  Meteoric  theory  of  the  repair  of 
Solar  Heat,  to  be  noticed  presently. 

III.  The  hypothesis  must  be  applicable  to  the  descrip- 


HYPOTIIESIS. 


107 


f 


t 


tion  or  explanation  of  all  the  observed  phenomena,  and, 
if  it  assign  a  cause,  must  assign  a  cause  fully  adequate 
to  have  produced  them.  A  hypothesis,  which  does  not 
satisfy  this  requirement,  may  be  at  once  rejected.  Thus, 
when  the  circular  theory  of  planetary  motion  was  found 
inapplicable  to  describe  several  of  the  phenomena,  it 
was  rightly  abandoned,  and  the  theory  of  epicycles  and 
eccentrics,  which,  though  erroneous,  was  fully  adequate 
to  explain  all  the  known  phenomena,  was  substituted  for 
it.  One  of  the  most  familiar  instances  of  an  inadequate 
hypothesis  is  the  theory  started  by  Voltaire,  there  is  little 
doubt  in  irony,  that  the  marine  shells  found  on  the  tops 
of  mountains  are  Eastern  species,  dropped  from  the  hats 
of  pilgrims,  as  they  returned  from  the  Holy  Land.  Such 
a  theory  would  obviously  be  inadequate  to  account  (i)  for 
the  numbers  of  the  shells,  (2)  for  the  fact  that  they  are 
found  imbedded  in  the  rocks,  (3)  for  their  existence  far 
away  from  the  tracks  of  pilgrims,  to  say  nothing  of  the 
fact  that  many  of  these  shells  bear  no  resemblance  to 
recent  Eastern  species,  while  none  resemble  them  exactly. 
The  contrast  between  an  adequate  and  an  i?tadequate 
hypothesis  is  well  illustrated  by  two  of  the  rival  hypo- 
theses by  which  it  is  attempted  to  account  for  the  gener- 
ation and  the  maintenance  of  solar  heat.  These  are 
respectively  the  Meteoric  Theory  and  the  Theory  of 
Chemical  Combustion.  In  speaking  of  the  former 
theory.  Professor  Tyndall  says  ^'  : — 

"  Ileal  a  Mode  of  Motion,   3rd  ed.  §§  689-693.      Sir  William 
Thomson,  however,  from  various  considerations,  arrived  at  the  con- 


Io8     PROCESSES  SUBSIDIARY  TO  INDUCTION', 

*  I  have  already  alluded  to  another  theory,  which,  however 
bold  it  may  at  first  sight  appear,  deserves  our  serious  atten- 
tion— the  Meteoric  Theory  of  the  Sun.  Kepler's  celebrated 
statement,  that  "there  are  more  comets  in  the  heavens  than 
fish  in  the  ocean,"  implies  that  a  small  portion  only  of  the 
total  number  of  comets  belonging  to  our  system  are  seen 
from  the  earth.  But  besides  comets,  and  planets,  and  moons, 
a  numerous  class  of  bodies  belong  to  our  system  which,  from 
their  smallness,  might  be  regarded  as  cosmical  atoms.  Like 
the  planets  and  the  comets,  these  smaller  asteroids  obey  the 
law  of  gravity,  and  revolve  in  elliptic  orbits  round  the  sun. 
It  is  they  which,  when  they  come  within  the  earth's  atmo- 
sphere, and  are  fired  by  friction,  appear  to  us  as  meteors  and 
falling  stars. 

*  On  a  bright  night,  twenty  minutes  rarely  pass  at  any  part 
of  the  earth's  surface,  without  the  appearance  of  at  least  one 
meteor.  Twice  a  year  (on  the  12th  of  August  and  14th  of 
November)  they  appear  in  enormous  numbers.  During  nine 
hours  in  Boston,  when  they  were  described  as  falling  as  thick 
as  snowflakes,  240,000  meteors  were  observed  The  number 
falling  in  a  year  might,  perhaps,  be  estimated  at  hundreds  or 
thousands  of  millions,  and  even  these  would  constitute  but 
a  small  portion  of  the  total  crowd  of  asteroids  that  circulate 
round  the  sun.  From  the  phenomena  of  light  and  heat,  and 
by  direct  observation  on  Encke's  comet'  (the  inference  from 
which  '  observation,'  however,  it  may  be  remarked,  is  very 
doubtful),  *  we  learn  that  the  universe  is  filled  by  a  resisting 

elusion  that  '  the  sun's  expenditure  [of  heaij,  though  originated,  is 
not  maintained  by  mechanical  impact ;  the  low  rate  of  cooling  and 
the  consequent  constancy  of  the  emission  being  considered  by  him 
as  due,  in  great  part,  to  the  high  specific  heat  of  the  matter  of  the 
sun.'  See  Tyndall's  Heat,  &c.,  §  701.  Other  physicists  ;see  Young 
on  the  Sun,  j)p.  270-7'  conjecture  that  the  heat  of  the  sun  is  partly 
due  to  its  gradual  contiaclion  and  the  increase  of  temperature  thus 
generated. 


HYPOTHESIS. 


109 


medium,  through  the  friction  of  which  all  the  masses  of  our 
system  are  drawn  gradually  towards  the  sun.  And  though 
the  larger  planets  show,  in  historic  times,  no  diminution  of 
their  periods  of  revolution,  it  itiay  be  otherwise  with  the 
smaller  bodies.  In  the  time  required  for  the  mean  distance 
of  the  earth  to  alter  a  single  yard,  a  small  asteroid  may  have 
approached  thousands  of  miles  nearer  to  the  sun. 

'  Following  up  these  reflexions,  we  should  be  led  to  the 
conclusion  that,  while  an  immeasurable  stream  of  ponderable 
meteoric  matter  moves  unceasingly  towards  the  sun,  it  must 
augment  in  density  as  it  approaches  its  centre  of  convergence. 
And  here  the  conjecture  naturally  rises,  whether  that  vast 
nebulous  mass,  the  Zodiacal  Light,  which  embraces  the  sun, 
may  not  be  a  crowd  of  meteors.  It  is  at  least  proved  that  this 
luminous  phenomenon  arises  from  matter  which  circulates 
in  obedience  to  planetary  laws  ;  hence,  the  entire  mass  of  the 
zodiacal  light  must  be  constantly  approaching,  and  incessantly 
raining  its  substance  down  upon  the  sun. 

*  It  is  easy  to  calculate  both  the  maximuin  and  the  minimum 
velocity,  imparted  by  the  sun's  attraction  to  an  asteroid  circu- 
lating round  him.  The  maximum  is  generated  when  the  body 
approaches  the  sun  from  an  infinite  distance  ;  the  entire puU 
of  the  sun  being  then  exerted  upon  it.  The  minimum  is  that 
velocity  which  would  barely  enable  the  body  to  revolve  round 
the  sun  close  to  his  surface.  The  final  velocity  of  the  former, 
just  before  striking  the  sun,  would  be  390  miles  a  second,  that 
of  the  latter  276  miles  a  second.  The  asteroid,  on  striking 
the  sun,  with  the  former  velocity,  would  develope  more  than 
9C00  times  the  heat  generated  by  the  combustion  of  an  equal 
asteroid  of  solid  coal ;  while  the  shock,  in  the  latter  case, 
would  generate  eat  equal  to  that  of  the  combustion  of  up- 
wards of  4000  such  asteroids.  It  matters  not,  therefore, 
whether  the  substances  falling  into  the  sun  be  combustible  or 
not ;  their  being  combustible  would  not  add  sensibly  to  the 
tremendous  heat  produced  by  their  mechanical  collision. 


no    PROCESSES  SUBSIDIARY  TO  INDUCTION, 

*  Here,  then,  we  have  an  agency  competent  to  restore  his 
lost  energy  to  the  sun,  and  to  maintain  a  temperature  at  his 
surface  which  transcends  all  terrestrial  combustion.  In  the 
fall  of  asteroids  we  find  the  means  of  producing  the  solar  light 
and  heat.  It  may  be  contended  that  this  showering  down  of 
matter  necessitates  the  growth  of  the  sun  :  it  does  so ;  but 
the  quantity  necessary  to  maintain  the  observed  calorific 
emission  for  4000  years,  would  defeat  the  scrutiny  of  our  best 
instruments.  If  the  earth  struck  the  sun,  it  would  utterly 
vanish  from  perception ;  but  the  heat  developed  by  its  shock 
would  cover  the  expenditure  of  a  century.' 

Of  the  other  theory,  Professor  Tyndall  says  ^'^ : — 

'Sir  William  Thomson  adduces  the  following  forcible 
considerations  to  show  the  inadequacy  of  chemical  com- 
bination to  produce  the  sun's  heat.  "  Let  us  consider,"  he 
says,  "how  much  chemical  action  would  be  required  to 
produce  the  same  effects.  .  .  .  Taking  the  former  estimate, 
2781  thermal  units  *=*  centigrade  (each  1390  foot  pounds) 
or  3,869,000  foot  pounds,  which  is  equivalent  to  7000  horse- 
power, as  the  rate  per  second  of  emission  of  energy  from 
every  square  foot  of  the  sun's  surface,  we  find  that  more 
than  0.42  of  a  pound  of  coal  per  second,  1500  lbs.  per  hour, 
would  be  required  to  produce  heat  at  the  same  rate.  Now 
if  all  the  fires  of  the  whole  Baltic  fleet  (this  was  written  in 
1854)  were  heaped  up  and  kept  in  full  combustion  over  one 
or  two  square  yards  of  surface,  and  if  the  surface  of  a  globe 
all  round  had  every  square  yard  so  occupied,  where  could 

*2  Ilea^  a  Mode  of  Motion,  §  700. 

*^  The  thermal  unit  is  the  quantity  of  heat  necessarj'  to  raise  the 
temperature  of  a  pound  of  water  one  degree.  If  the  degree  be  centi- 
grade, this  is  efiuivalcnt  to  the  heat  generated  by  a  pound  weij:jht 
falling  from  a  heii,'ht  of  1390  feet  against  the  earth.  The  K^xva  foot- 
pound expresses  the  energy  requisite  to  lift  one  pound  to  the  heiL;hl 
of  a  foot. 


HYPOTHESIS, 


III 


a  sufficient  supply  of  air  come  from  to  sustain  the  com- 
bustion ?  Yet  such  is  the  condition  we  must  suppose  the 
sun  to  be  in,  according  to  the  hypothesis  now  under  con- 
sideration. ...  If  the  products  of  combustion  were  gaseous, 
they  would,  in  rising,  check  the  necessary  supplies  of  fresh 
air  ;  if  they  were  solid  and  liquid  (as  they  might  be  if  the 
fuel  were  metallic),  they  would  interfere  with  the  supply  of 
elements  from  below.  In  either  or  in  both  ways,  the  fire 
would  be  choked,  and  I  think  it  may  be  safely  affirmed  that 
no  such  fire  could  keep  alight  for  more  than  a  few  minutes, 
by  any  conceivable  adaptation  of  air  and  fuel.  If  the  sun 
be  a  burning  mass  it  must  be  more  analogous  to  burning 
gunpowder  than  to  a  fire  burning  in  air ;  and  it  is  quite 
conceivable  that  a  solid  mass,  containing  within  itself  all  the 
elements  required  for  combustion,  provided  the  products  of 
combustion  are  permanently  gaseous,  could  burn  off  at  its 
surface  all  round,  and  actually  emit  heat  as  copiously  as  the 
sun.  Thus,  an  enormous  globe  of  gun-cotton  might,  if  at 
first  cold,  and  once  set  on  fire  round  its  surface,  get  to  a 
permanent  rate  of  burning,  in  which  any  internal  part  would 
become  heated  sufficiently  to  ignite,  only  when  nearly  ap- 
proached by  the  burning  surface.  It  is  highly  probable 
indeed  that  such  a  body  might  for  a  time  be  as  large  as  the 
sun  and  give  out  luminous  heat  as  copiously,  to  be  freely 
radiated  into  space,  without  suffering  more  absorption  from 
its  atmosphere  of  transparent  gaseous  products  than  the  light 
of  the  sun  actually  does  experience  from  the  dense  atmo- 
sphere through  which  it  passes.  Let  us  therefore  consider 
at  what  rate  such  a  body,  giving  out  heat  so  copiously,  would 
bum  away  ;  the  heat  of  combustion  could  probably  not  be  so 
much  as  4000  thermal  units  per  pound  of  matter  burned,  the 
greatest  thermal  equivalent  of  chemical  action  yet  ascertained 
falling  considerably  short  of  this.  But  2781  thermal  units 
(as  found  above)  are  emitted  per  second  from  each  square 
foot  of  the  sun ;  hence  there  would  be  a  loss  of  about  0.7 


112     PROCESSES  SUBSIDIARY  TO  INDUCTION', 

of  a  pound  of  matter  per  square  foot  per  second  ...  or 
a  layer  half  a  foot  thick  in  a  minute,  or  55  miles  thick  in 
a  year.  At  the  same  rate  continued,  a  mass  as  large  as  the 
sun  is  at  present  would  burn  away  in  8000  years.  If  the  sun 
has  been  burning  at  that  rate  in  past  time  he  must  have  been 
of  double  diameter,  of  quadruple  heating  power,  and  of  eight- 
fold mass  only  8000  years  ago.  We  may  therefore  quite 
safely  conclude  that  the  sun  does  not  get  its  heat  by  chemical 
action  .  .  .  and  we  must  therefore  look  to  the  meteoric  theory 
for  fuel." ' 


A  hypothesis  which  fulfils  these  three  conditions  is  a 
legitimate  hypothesis^  though  it  must  conform  to  still  more 
rigorous  requirements  before  it  can  be  accepted  as  a 
complete  Induction,  or  even  be  regarded  as  possessing 
any  great  amount  of  probability.  Thus,  the  Meteoric 
Theory,  though  it  is  not  yet  proved^  and  perhaps  never 
may  be  proved,  to  be  the  true  explanation  of  the  pheno- 
menon of  solar  heat,  is  perfectly  tenable  as  a  hypothesis. 
For,  to  take  the  conditions  in  the  reverse  order  to  that 
in  which  they  have  been  enumerated  above,  the  impact 
of  a  large  number  of  meteors  on  a  body  of  considerable 
density,  such  as  the  sun  probably  is,  would  be  competent 
or  adequate  to  produce  the  given  effect ;  the  theory  in 
question  is  likely,  if  not  to  be  proved  or  disproved, 
at  least  to  be  rendered  more  or  less  probable  by  the 
progress  of  astronomical  science  ;  lastly,  we  do  not  know, 
nor  have  we  any  reason  to  suppose,  that  the  hypothesis 
is  an  untrue  explanation  of  the  facts.  But,  though  legi- 
timate as  a  hypothesis,  before  we  could  accept  the 
Meteoric   theory   as  a   Valid   or    Complete   Induction, 


HYPOTHESIS. 


113 


that  is  to  say,  an  ascertained  truth,  we  should  require 
to  know  not  only  that  there  is  a  large  number  of  meteors 
circulating  round  the  sun,  that  these  meteors  have  a 
tendency  to  fall  into  the  centcal  body,  and  that,  //  they 
were  falling  or  had  fallen  in  sufficient  quantities,  they 
would  be  competent  or  would  have  been  competent  to 
produce  the  present  amount  of  solar  heat,  but  also  that 
they  do,  as  a  matter  of  fact,  fall  in  sufficient  quantities 
to  account  for  the  phenomenon,  or,  at  least,  that  nothing 
else  but  the  showering  down  of  asteroids  and  meteors 
could  account  for  it. 

It  was  by  availing  himself  of  the  latter  mode  of  proof 
that  Newton  demonstrated  the  existence  in  the  sun  of  a 
central  force  attracting  the  planets  towards  it.    Assuming 
Kepler's  hypothesis  (then  sufficiently  verified  by  obser- 
vation to  be  universally  accepted  as  a  true  statement 
of  the  facts),  that  equal  areas  are  described  by  the  radii 
vectores  of  the  planets  in  equal  times,  Newton  showed 
that  this  fact  could  be  due  to  only  one  cause,  namely, 
the  deflexion  of  the  planets  from  their  rectilinear  course 
by  a  force  acting  in  the  direction  of  the  sun's  centre. 
The  existence  of  the  central  force  was,  at  first,  started 
by  him  as  a  hypothesis.     *  He  then  proved  that,'  on  the 
supposition  of  the  existence  of  such  a  force,  '  the  planet 
will  describe,  as  we  know  by  Kepler's  first  law  that  it 
does  describe,  equal  areas  in  equal  times ;  and,  lastly, 
he  proved  that  if  the  force  acted  in  any  other  direction 
whatever,  the  planet  would  not  describe  equal  areas  in 
equal  times.     It  being  thus  shown  that  no  other  hypo- 


114     PROCESSES  SUBSIDIARY  TO  INDUCTION'. 

thesis  would  accord  with  the  facts,  the  assumption  was 
proved  ;  the  hypothesis  became  an  inductive  truth.  Not 
only  did  Newton  ascertain  by  this  hypothetical  process 
the  direction  of  the  deflecting  force  ;  he  proceeded  in 
exactly  the  same  manner  to  ascertain  the  law  of  variation 
of  the  quantity  of  that  force.  He  assumed  that  the  force 
varied  inversely  as  the  square  of  the  distance  ;  showed 
that  from  this  assumption  the  remaining  two  of  Kepler's 
laws  might  be  deduced  ;  and  finally,  that  any  other  law 
of  variation  would  give  results  inconsistent  with  those 
laws,  and  inconsistent,  therefore,  with  the  real  motions 
of  the  planets,  of  which  Kepler's  laws  were  known  to  be 
a  correct  expression  **.* 

It  will  be  noticed  that  the  course  of  demonstration 
pursued  in  this  instance  is  the  following:  (i)  we  have 
certain  observed  facts  \  (2)  these  observed  facts  are 
generalised  in  what  are  called  Kepler's  Laws;  (3)  we 
have  the  assumption  of  the  central  force  ;  (4)  it  is  shown 
that  the  central  force  will  account  for  Kepler's  Laws, 
and  therefore,  of  course,  for  the  particular  facts  of  ob- 
servation on  which  those  Laws  were  founded ;  (5)  it  is 
shown  (and  this,  together  with  the  next  step,  is  what 
properly  constitutes  the  demonstration)  that  this  assump- 
tion is  the  only  one  which  will  account  for  the  Laws  or 
the  particular  facts  expressed  by  them ;  (6)  it  is  inferred 
inductively,  by  means  of  the  Method  of  Difference  (to  be 
hereafter  described),  that  the  assumption  of  the  central 
force,  as  it  will  account  for,  and  is  the  only  supposition 
*♦  Mill's  Logic,  Bk.  III.  ch.  xiv.  §  4. 


HYPOTHESIS. 


II 


which  will  account  for,  the  observed  facts,  must  be 
accepted  as  true  ;  (7)  Kepler's  Laws  (which  had  hitherto 
been  accepted  as  correct  statements  of  observed  facts, 
though  they  had  not  yet  been  explained  by  reference 
to  any  cause  competent  to  account  for  them)  are  now 
proved  deductively  from  what  we  have  ascertained  to  be 
the  Valid  Induction  of  the  Central  Force. 

A  Hypothesis  can  only  be  converted  into  a  Valid 
Induction  ^^  by  the  application  of  one  or  other  of  the 
Inductive  Methods  (to  be  described  in  the  next  Chapter), 
or,  if  we  insist  on  strict  accuracy  of  proof,  of  such  of 
them  as  furnish  absolutely  certain  conclusions. 


Note  I. — According  to  the  view  here  taken,  which 
agrees  with  that  of  Mr.  Mill,  a  hypothesis  cannot  claim 
to  be  regarded  as  an  established  truth,  till  it  has  con- 
formed to  the  requirements  of  one  or  other  of  the 
inductive  methods,  or  has  been  shown  to  admit  of 
being  deduced  from  some  previously  established  In- 
duction. Thus,  when  Newton  proves  the  existence  of 
a  central  force,  deflecting  the  planets  from  the  recti- 
lineal course  which  they  would  otherwise  describe  and 

*^  Though  a  hypothesis  is  usually  contrasted  with  a  Valid  or 
Complete  Induction,  it  must  not  be  forgotten  that  we  have  admitted, 
as  legitimate,  hypotheses  which  are  never  likely  to  rest  on  more  than 
probable  evidence.  These  can,  of  course,  receive  accessions  of  proof 
only  by  the  same  means  as  those  by  which  we  establish  Imperfect 
Inductions.  It  should  also  be  remembered  that  the  truth  of  a 
hypothesis  may  be  demonstrated  by  deductive  as  well  as  by  induc- 
tive methods. 

I   2 


Il6     PROCESSES  SUBSIDIARY  TO  INDUCTION, 


HYPOTHESIS, 


117 


making  them  describe  curves  round  the  sun,  by  showing 
that  no  other  supposition  would  account  for  the  fact  that 
their  radii  vectores  describe  equal  areas  in  equal  times,  he 
is,  as  Mr.  Mill  says,  employing  the  Method  of  Difference.  < 
The  demonstration  *  affords  the  two  instances,  ABC, 
a  be,  and  B  C,  ^r.     A  represents  central  force  ;  A  B  C, 
the  planets ////5  a  central  force  ;  B  C,  the  planets  as  they 
would  be  without  a  central  force.     The  planets  with  a 
central  force  give  a  (areas  proportional  to  the  times), 
(together  with  other  effects  be)  ;  the  planets  without  a 
central  force  give  b  e  {2i  set  of  motions)  without  a.     This 
is  the  Method  of  Difference  in  all  its  strictness.   It  is  true, 
the  two  instances  which  the  method  requires  are  obtained 
in  this  case,  not  by  experiment,  but  by  a  prior  deduction. 
But  that  is  of  no  consequence.     It  is  immaterial  what  is 
the  nature  of  the  evidence  from  which  we  derive  the  as- 
surance that  ABC  will  produce  a  b  e,  and  B  C  only  b  e  ; 
it  is  enough  that  we  have  that  assurance.    In  the  present 
case,  a  process  of  reasoning  furnished  Newton  with  the 
very  instances,  which,  if  the  nature  of  the  case  had  ad- 
mitted of  it,  he  would  have  sought  by  experiment  *^' 

Dr.  Whewell,  who  does  not  acknowledge  the  utility  of 
Mr.  Mill's  methods,  appears  to  regard  the  inductive  pro- 
cess as  consisting  simply  in  the  framing  of  successive 
hypotheses,  the  comparison  of  these  hypotheses  with  the 
ascertained  facts  of  nature,  and  the  introduction  into 

*•  Mill's  logic,  Vk.  III.  ch.  xiv.  §  4.  I  have  slightly  altered  this 
passage,  as  it  stands  in  Mill,  and  as  it  stood  in  my  earlier  editions, 
so  as  to  make  it  plainer  to  the  student. 


them  of  such  modifications  as  that  comparison  may 
render  necessary  *'.  The  first  requisite  in  a  hypothesis, 
according  to  Dr.  Whewell,  is  that  it  shall  explain  all 
the  observed  facts.  But  its*  probability,  he  urges,  will 
be  considerably  enhanced,  if,  in  addition  to  explaining 
observed  facts,  it  enables  us  to  predict  the  future. 
*  Thus  the  hypotheses  which  we  accept  ought  to  explain 
phenomena  which  we  have  observed.  But  they  ought 
to  do  more  than  this  :  our  hypotheses  ought  to  foretell 
phenomena  which  have  not  yet  been  observed  ;  at  least 
all  phenomena  of  the  same  kind  as  those  which  the 
hypothesis  was  invented  to  explain.  For  our  assent  to 
the  hypothesis  implies  that  it  is  held  to  be  true  of  all 
particular  instances.  That  these  cases  belong  to  past 
or  to  future  times,  that  they  have  or  have  not  already 
occurred,  makes  no  difference  in  the  applicability  of  the 
rule  to  them.  Because  the  rule  prevails,  it  includes  all 
cases  ;  and  will  determine  them  all,  if  we  can  only  cal- 
culate its  real  consequences.  Hence  it  will  predict  the 
results  of  new  combinations,  as  well  as  explain  the  ap- 
pearances which  have  occurred  in  old  ones.  And  that  it 
does  this  with  certainty  and  correctness,  is  one  mode  in 
which  the  hypothesis  is  to  be  verified  as  right  and  useful'^' 

«'  A  theory  of  Induction  almost  identical  with  that  of  Dr.  Whewell 
(though,  I  venture  to  suggest,  not  so  clearly  stated  or  so  carefully 
guarded)  has  been  recently  propounded  by  Professor  Stanley  Jevons 
in  his  Principles  of  Science.  This  theory,  together  with  other  points 
of  difference  between  Professor  Jevons  and  myself,  I  have  noticed  in 
the  Preface  to  the  third  edition,  reprinted  in  the  present  one. 

**  Novum  Organon  Renovatum^  Bk.  II.  ch.  v.  art.  10. 


I 


Il8     PROCESSES  SUBSIDIARY  TO  INDUCTION. 

Curiously  enough,  the  first  hypothesis  which  Dr. 
Whewell  cites,  as  having  fulfilled  both  these  conditions, 
is  also  one  which  eventually  proved  to  be  false.  *  For 
example,  the  Epicyclical  Theory  of  the  heavens  was 
confirmed  by  its  predicting  truly  eclipses  of  the  sun 
and  moon,  configurations  of  the  planets,  and  other 
celestial  phenomena ;  and  by  its  leading  to  the  con- 
struction of  Tables  by  which  the  places  of  the  heavenly 
bodies  were  given  at  every  moment  of  time.  The  truth 
and  accuracy  of  these  predictions  were  a  proof  that  the 
hypothesis  was  valuable,  and,  at  least  to  a  great  extent, 
true ;  although,  as  was  afterwards  found,  it  involved  a 
false  representation  of  the  structure  of  the  heavens.'  A 
theory  may  thus  not  only  enable  us  to  explain  known 
facts,  but  even  to  predict  the  future,  and  still  be  untrue. 
Notwithstanding,  however,  the  infelicitous  character  of  the 
example  selected.  Dr.  Whewell  attaches  the  greatest  impor- 
tance to  the  fulfilment  of  this  condition  by  a  hypothesis. 
'  Men  cannot  help  believing  that  the  laws  laid  down  by 
discoverers  must  be  in  a  great  measure  identical  with  the 
real  laws  of  nature,  when  the  discoverers  thus  determine 
effects  beforehand  in  the  same  manner  in  which  nature 
herself  determines  them  when  the  occasion  occurs.  Those 
who  can  do  this  must,  to  a  considerable  extent,  have 
detected  nature's  secret ; — must  have  fixed  upon  the  con- 
ditions to  which  she  attends,  and  must  have  seized  the 
rules  by  which  she  applies  them.  Such  a  coincidence  of 
untried  facts  with  speculative  assertions  cannot  be  the 
work  of  chance,  but  implies  some  large  portion  of  truth 


HYPOTHESIS. 


119 


in  the  principles  on  which  the  reasoning  is  founded.  To 
trace  order  and  law  in  that  which  has  been  observed,  may 
be  considered  as  interpreting  what  nature  has  written 
down  for  us,  and  will  commonly  prove  that  we  under- 
stand her  alphabet.  But  to  predict  what  has  not  been 
observed,  is  to  attempt  ourselves  to  use  the  legislative 
phrases  of  nature;  and  when  she  responds  plainly  and 
precisely  to  that  which  we  thus  utter,  we  cannot  but  sup- 
pose that  we  have  in  a  great  measure  made  ourselves 
masters  of  the  meaning  and  structure  of  her  language. 
The  prediction  of  results,  even  of  the  same  kind  as  those 
which  have  been  observed,  in  new  cases,  is  a  proof  of  real 
success  in  our  inductive  processes.' 

But  what  appears  to  Dr.  Whewell  to  establish  the  truth 
of  a  hypothesis  beyond  all  question  is  what  he  calls  a 
Consilience  of  Inductions.  *  We  have  here  spoken  of  the 
prediction  of  facts  of  the  same  kind  as  those  from  which 
our  rule  was  collected.  But  the  evidence  in  favour  of  our 
induction  is  of  a  much  higher  and  more  forcible  character 
when  it  enables  us  to  explain  and  determine  cases  of 
a  kitid  different  from  those  which  were  contemplated  in 
the  formation  of  our  hypothesis.  The  instances  in  which 
this  has  occurred,  indeed,  impress  us  with  a  conviction 
that  the  truth  of  our  hypothesis  is  certain.  No  accident 
could  give  rise  to  such  an  extraordinary  coincidence.  No 
false  supposition  could,  after  being  adjusted  to  one  class 
of  phenomena,  exactly  represent  a  different  class,  where 
the  agreement  was  unforeseen  and  uncontemplated.  That 
rules  springing  from  remote  and  unconnected  quarters 


120     PROCESSES  SUBSIDIARY  TO   TNDUCTIOI^, 

should  thus  leap  to  the  same  point,  can  only  arise  from 
that  being  the  point  where  truth  resides. 

*  Accordingly  the  cases  in  which  inductions  from  classes 
of  facts  altogether  different  have  thus  jumped  to^^ether, 
belong  only  to  the  best  established  theories  which  the 
history  of  science  contains.  And,  as  I  shall  have  occasion 
to  refer  to  this  peculiar  feature  in  their  evidence,  I  will 
take  the  liberty  of  describing  it  by  a  particular  phrase ; 
and  will  term  it  the  Consilience  of  Inductions. 

*  It  is  exemplified  principally  in  some  of  the  greatest 
discoveries.  Thus  it  was  found  by  Newton  that  the 
doctrine  of  the  Attraction  of  the  Sun  varying  according 
to  the  Inverse  Square  of  the  distance,  which  explained 
Kepler's  Third  Law,  of  the  proportionality  of  the  cubes 
of  the  [mean]  distances  to  the  squares  of  the  periodic 
times  of  the  planets,  explained  also  his  First  and  Second 
Laws,  of  the  elliptical  motion  of  each  planet ;  although 
no  connexion  of  these  laws  had  been  visible  before. 
Again,  it  appeared  that  the  force  of  Universal  Gravitation, 
which  had  been  inferred  from  the  Perturbations  of  the 
moon  and  planets  by  the  sun  and  by  each  other,  also 
accounted  for  the  fact,  apparently  altogether  dissimilar 
and  remote,  of  the  Precession  of  the  equinoxes.  Here 
was  a  most  striking  and  surprising  coincidence,  which 
gave  to  the  theory  a  stamp  of  truth  beyond  the  power 
of  ingenuity  to  counterfeit  *^' 

It  is  undeniable  that  a  theory  which  thus  appears  to 
afford  an  explanation  of  different  classes  of  facts  strikes 
*"  Novum  Orgauon  Renovatum,  Bk.  II.  ch.  v.  art.  ii. 


HYPOTHESIS, 


121 


) 


the  imagination  with  considerable  force,  and  that  its  very 
simplicity  furnishes  prima  facie  evidence  of  its  truth. 
But  what  is  required  before  a  hypothesis  can  be  placed 
beyond  suspicion  is  formal  jfroof,  and  that,  it  appears 
to  me,  is  furnished  by  Mr.  Mill's  'methods,'  and  not 
by  Dr.  Whewell's  requisitions  of  explanation,  prediction, 
and  consilience  of  inductions.  For  the  questions  at  issue 
between  Mr.  Mill  and  Dr.  Whewell,  see  Whewell's 
Novum  Organon  Renovatum  (where  his  views  are  stated 
in  their  latest  and  most  matured  form),  Bk.  II.  ch.  v. 
§  3,  and  Mill's  Logic,  Bk.  III.  ch.  xiv.  §  6. 

jSfote  2. — In  attempting  to  determine  the  conditions 
to  which  a  legitimate  hypothesis  must  conform,  I  have 
avoided  the  employment  of  the  expressions  vera  causa 
and  adccquata  causa.  In  the  first  place,  a  hypothesis  may 
simply  attempt  to  find  a  general  expression  for  a  number 
of  isolated  facts  without  referring  them  to  any  cause,  as 
was  the  case  with  the  various  hypotheses  respecting  the 
shape  of  the  planetary  orbits,  and  hence  to  speak  as  if 
a  hypothesis  always  assigned  a  cause  is  an  undue  limita- 
tion of  the  meaning  of  the  word.  But  to  the  expression 
vera  causa  there  is  a  more  special  exception.  Its  meaning 
is  ambiguous.  Is  it  the  actual  cause  which  produces  a 
phenomenon,  or  a  cause  which  we  know  to  be  actually 
existent,  or  a  cause  analogous  to  an  existent  cause? 
The  student  will  find  a  criticism  of  this  expression  (first 
employed  by  Newton)  in  Dr.  Whewell's  Philosophy  of 
Discovery,  ch.  xviii.  §  5,  &c.      The   expression  cannot 


122     PROCESSES  SUBSIDIARY  TO  INDUCTION-, 

have  been  used  in  the  first,  which  is  its  most  obvious, 
sense,  for,  as  Dr.  Whewell  says,  'although  it  is  the 
philosopher's  aim  to  discover  such  causes,  he  would  be 
little  aided  in  his  search  of  truth,  by  being  told  that  it 
is  truth  which  he  is  to  seek.'  But  in  the  second  of  the 
two  remaining  senses,  the  requirement,  as  would  now 
be  generally  acknowledged,  is  too  stringent,  and,  if  it 
had  been  invariably  observed,  would  have  prevented  us 
from  reaping  some  of  the  greatest  discoveries  in  science, 
while  in  the  last  it  is  so  vague  as  to  be  of  no  practical 
service.  It  has  been  attempted  to  affix  other  meanings 
to  the  phrase  ;  but  there  can  be  little  doubt  that  Newton, 
having  in  mind  the  Vortices  of  Descartes,  intended  to 
protest  against  the  introduction  of  causes  of  whose  ex- 
istence we  have  no  direct  knowledge,  and  consequently 
laid  down  a  rule,  which  the  subsequent  history  of  science 
has  shown  to  be  needlessly  stringent. 

Note  3. — We  sometimes  find  the  expression  a  'gra- 
tuitous hypothesis.'  By  this  phrase  is  meant  the  assump- 
tion of  an  unknown  cause,  when  the  phenomenon  is 
capable  of  being  explained  by  the  operation  of  known 
causes,  or  the  introduction  of  an  extraneous  (though  it 
may  be  known)  cause,  when  the  phenomenon  is  capable 
of  being  accounted  for  by  the  causes  already  known  to 
be  in  operation.  Of  the  latter  case  we  should  have 
instances,  where  a  man  is  supposed  to  have  acted  at  the 
suggestion  of  another,  though  his  own  motives  would 
supply  a  sufficient  explanation  of  his  conduct,  or  where 


HYPOTHESIS. 


123 


a  man  is  supposed  to  have  been  poisoned,  though  he  was 
already  known  to  have  been  suffering  from  a  fatal  disease. 
Of  the  former  case  we  should  have  instances  in  the 
crystalline  spheres  of  the  ancient  astronomers  and  in  the 
masses  of  crystal  which  were  supposed  by  Lodovico  delle 
Colombe  to  fill  up  the  cavities  of  the  moon  (there  being 
no  instances  known  to  us  of  the  existence  of  crystal  in 
these  huge  masses,  and  the  phenomena  being  capable 
of  explanation  without  making  the  supposition) ;  in  the 
caloric  (which  was  supposed  to  be  a  distinct  substance) 
of  the  early  writers  on  heat ;  in  the  *  electrical  fluid '  of 
the  early  electricians  ;  and  in  the  imoplioiai  of  Democritus 
or  the  'intentional  species'  of  the  Peripatetics,  which, 
being  invented  for  the  purpose  of  explaining  the  per- 
ception of  material  objects  by  the  mind,  were  themselves 
equally  in  need  of  explanation.  In  all  these  instances, 
under  whichever  of  the  two  cases  they  may  fall,  the 
objection  to  the  hypothesis  is  that  it  seems  'not  to  be 
needed.' 

I  have  said  nothing  of  'gratuitous  hypotheses '  in  the 
text,  as  a  hypothesis,  though  it  may  appear  to  be  gra- 
tuitous, may  still  be  legitimate,  and  may  even  ultimately 
turn  out  to  be  true. 


CHAPTER  III. 

On  the  Inductive  Methods, 

INDUCTION  has  been  defined  to  be  a  legitimate 
inference  from  the  known  to  the  unknown.  But  the 
unknown  must  not  be  entirely  unknown.  It  must  be 
known  to  agree  in  certain  circumstances  with  the  known, 
and  it  is  in  virtue  of  this  agreement  that  the  inference 
is  made.  Now,  how  are  we  to  ascertain  what  are  the 
common  circumstances  which  justify  the  inductive  infer- 
ence ?  X  and  Y  may  both  agree  in  exhibiting  the  circum- 
stances a,  b,  c,  but  it  will  not  follow  because  X  exhibits 
the  quality  m,  that  therefore  this  quality  will  also  neces- 
sarily be  found  in  Y.  Nor  even,  if  twenty,  thirty,  a 
hundred,  or  a  thousand  cases  could  be  adduced  in  which 
the  circumstances  a,  b,  c  were  found  to  be  accompanied 
by  the  circumstance  w,  would  it  follow  necessarily  (it 
might  not  even  follow  probably)  that  the  next  case  in 
which  we  detected  the  circumstances  a,  b,  c  would  also 
exhibit  the  quality  m.  We  might  pass  through  a  field  con- 
taining thousands  of  blue  hyacinths,  but  this  fact  would 
not  justify  us  in  expecting  that  the  next  time  we  saw 


\ 


INDUCTIVE  METHODS, 


12!^ 


a  hyacinth,  it  would  be  a  blue  one.     This  form  of  induc- 
tion {Inductio  per  Enumerationeffi  Simplicetn)  may  have  no 
value  whatever.  In  most  cases,  the  condemnation  passed 
on   it  by  Bacon  *  is  perfectly  jtist :  '  Inductio  quae  pro- 
cedit  per  enumerationem  simplicem,  res  puerilis  est,  et 
precario  concludit,  et  periculo  exponitur  ab  instantia  con- 
tradictoria,  et  plerumque  secundum  pauciora  quam  par 
est,  et  ex  his  tantummodo  quae  praesto  sunt,  pronunciat.' 
But  when  we  have  reason  to  think  that  any  instances  to 
the  contrary,  if  there  were  such,  would  be  known  to  us,  the 
argument  may  possess  considerable  value,  and  when,  as  in 
the  case  of  the  Laws  of  Causation  and  of  the  Uniformity 
of  Nature,  we  feel  certain,  from  a  wide  and  uncontra- 
dicted experience,  that  there  are  no  cases  to  the  contrary, 
no  stronger  argument  (to  us  individually)  can  be  adduced. 
It  is  not  often,  however,  that  an  Inductio  per  Enumera- 
tionem Simplicem  can  afford  us  this  certainty^      Our 
trustworthy  inductions  are,  in  the  majority  of  cases,  the 
result  of  our  detecting  some  fact  of  causation  among  the 
observed  phenomena.  We  find,  for  instance,  that,  amongst 
the  observed  phenomena,  a,  b,  c,  ^  of  X,  a  is  the  cause 
of  r,  and,  consequently,  if  we  observe  the  phenomenon 
a  in  Y,  we  infer  that,  if  there  are  no  counteracting  cir- 
cumstances, Y  will  possess  the  quality^  as  well;  or,  if  we 

*  Novum  Organi4m,  Lib.  I.  aph.  cv. 

2  It  must  be  remembered  that  a  complete  enumeration  of  instances, 
when  we  know  the  enumeration  to  be  complete,  inasmuch  as  it  leaves 
no  room  for  an  inference  from  the  known  to  the  unknown,  does  not 
furnish  an  inductive  but  a  deductive  argument.  See  Elements  of  De- 
ductive Logic,  Part  III.  ch.  i.  appended  Note  2. 


126 


INDUCTIVE  METHODS, 


observe  the  phenomenon  c  in  Y,  we  infer  that  it  is  not 
unHkely^  that  a  may  be  present  as  well.  The  problem 
of  Induction,  therefore,  resolves  itself  (except  in  the 
cases  in  which  we  may  legitimately  employ  Inductio  per 
Enumerationem  Simplicem,  or  the  cases  in  which  we  have 
no  other  resource)  into  the  problem  of  detecting  facts  of 
Causation.  Certain  rules  for  this  purpose  have  been  laid 
down  by  Mr.  Mill,  called  by  him  the  Experimental 
Methods,  but  which  I  shall  describe  as  the  Inductive 
Methods. 

These  Methods,  it  will  be  noticed  as  we  proceed,  are  all 
methods  of  elimination^  or  devices  by  which  we  are  enabled 
to  argue  from  a  comparatively  small  number  of  instances 
with  the  same  certainty  as  if  they  were  ever  so  numerous. 

Before  proceeding  to  state  and  explain  these  Rules  or 
Methods,  it  may  be  useful  to  make  some  preliminary 
remarks  on  the  nature  of  the  causal  relations  which 
subsist  among  phenomena. 

(i)  The  same  cause,  unless  there  are  counteracting 
circumstances,  that  is,  other  causes  which  prevent  it  from 
acting  or  which  modify  its  action,  is  invariably  followed 
by  the  same  effect. 

(2)  As  already  shown  (Chapter  I.  pp.  13-16),  several 
causes  may  have  co-operated  in  producing  any  given 
effect.  In  this  case,  it  is  not  unusual  to  speak  of  the 
*  combination  of  causes  '  or  the  *  sum  of  the  causes.' 

*  I  say  'not  unlikely,'  for  c  might  be  due  to  some  other  cause  as 
well  as  a,  and,  therefore,  the  presence  of  c  does  not  enable  us  to  infer 
with  certainty  the  presence  of  a,  as  does  that  of  a  the  presence  of  c. 


INDUCTIVE   METHODS, 


127 


(3)  The  same  effect  may  be  due  to  several  distinct 
causes,  or  combinations  of  causes,  being  due  sometimes 
to  one  and  sometimes  to  another,  and,  hence,  though  we 
may  always  argue  from  a  particular  cause  to  its  effect,  w^e 
cannot  always  argue  from  an  effect  to  any  particular 
cause.  Thus,  ignition  may  be  due,  not  only  to  the  con- 
centration of  the  rays  of  solar  heat,  but  also  to  friction, 
electricity,  &c.  This  fact  has  given  occasion  to  the 
expression  'Plurality  of  Causes^  for  which  a  recent 
writer  (Mr.  Carveth  Read)  has  proposed  to  substitute 
the  expression  *  Vicariousness  of  Causes,'  in  order  to 
distinguish  clearly  the  case  of  alternative  from  that  of 
co-operating  or  concurrent  causes,  noticed  in  the  last 
paragraph  \ 

*  It  is  sometimes  doubted  whether  the  same  effect  is  ever  really 
due  to  different  causes,  and  it  may  be  conceded,  I  think,  that  dif- 
ferent causes  never  do  produce  precisely  the  same  aggregate  of  effects. 
Together  with  certain  common  effects,  they  produce  certain  divergent 
effects,  and  it  is  the  presence  of  these,  indeed,  that  enables  us  to 
determine  the  particular  cause  which  has  been  at  work  in  the  par- 
ticular instance.  There  is,  however,  nothing  in  this  circumstance 
inconsistent  with  the  occurrence  of  some  one  or  more  effects  common 
to  all  the  ciuses.  Thus,  the  whole  group  of  effects  produced  severally 
by  heat,  electricity,  impact,  differs  widely,  but,  at  the  same  time, 
the  motion  of  a  needle  may  be  a  common  part  of  the  effect  in  all 
three  instances,  and,  when  we  see  the  needle  in  motion,  we  may  be 
unable  to  say  to  which  of  the  three  causes  motion  is  due.  Similar 
considerations  may  be  applied  to  the  cases  of  ignition,  and  death, 
which  are  favourite  illustrations  of  the  operation  of  a  plurality  of 
causes.  Taking  A,  B,  C,  D  as  causes  or  combinations  of  causes,  and 
fl,  b,  c,  &c.  as  individual  portions  of  the  aggregate  effects  produced 
by  the  causes,  we  may  conceive  A  as  producing  a  d  c  d  e,  ]i  as  pro- 


128 


INDUCTIVE  METHODS. 


(4)  It  frequently  happens  that  between  the  original 
cause  and  the  ultimate  effect  there  intervene  a  number 
of  intermediate  causes.  Thus,  suppose  we  make  an 
experiment  by  which  motion  is  converted  into  heat,  heat 
into  electricity,  and  electricity  into  chemical  affinity;  we 
may,  roughly  speaking,  say  that  motion  has  been  the 
cause  of  the  chemical  affinity,  or  chemical  affinity  the 
effect  of  the  motion,  but,  speaking  strictly,  we  ought  to 
enumerate  the  intervening  causes. 

(5)  Sometimes  a  number  of  effects  appear  to  be 
produced  simultaneously  by  the  same  cause.  Thus,  it 
would  appear  that  there  are  many  cases  in  which,  if  one  of 
the  agents,  motion,  heat,  light,  electricity,  magnetism,  and 
chemical  affinity,  is  excited,  the  rest  are  developed  simul- 

ducing  defg  h,  C  as  producing  c  dei  k  l,D  z,?,  producing  e  in  n  0. 
In  this  case,  e  may  be  regarded  as  an  effect  due  to  any  one  of  the 
causes  A,  B,  C,  D,  though  the  'attendant  circumstances,'  as  they  are 
often  called,  are  widely  different  in  each  instance.  If,  therefore,  we 
were  to  state  the  doctrine  of  Plurality  or  '  Vicariousness  '  of  Causes 
exactly,  we  should  say,  not  that  the  same  effect  may  be  due  to  dif- 
ferent causes,  but  that,  of  the  total  effects  due  to  different  causes,  a 
certain  portion  is  often  found  to  be  common  to  all.  For  purposes 
of  practice,  however,  the  ordinary  mode  of  statement  is  sufficiently 
precise. 

It  seems  hardly  necessary  to  remark  that  it  is  no  valid  objection 
to  the  doctrine  of  Plurality  of  Causes  that  we  are  sometimes  able  to 
detect  between  the  alternative  causes  and  the  identical  effect  some 
set  of  conditions  which  is  the  same  in  all  cases.  This  discovery  only 
removes  the  plurality  of  causation  one  step  further  back,  and  the 
doctrine  can  only  be  consistently  denied  by  those  who  maintain  that 
at  no  single  point  in  the  series  of  receding  causes  can  we  find  the 
same  effect  produced,  or  capable  of  being  produced,  by  distinct 
causes. 


INDUCTIVE  METHODS, 


129 


taneously  '\  These  simultaneous  effects,  whether  we 
conceive  that  they  are  really  or  only  apparently  simul- 
taneous, would  be  called  joint  or  common  effects  of  the 
cause.  Similarly  the  expression  '  joint  effects  '  would  be 
employed  for  the  effects  produced  by  the  same  cause  on 
different  bodies,  or  different  portions  of  the  same  body. 
Thus,  if  a  blow  bruises  my  forehead,  and  at  the  same  time 
gives  me  a  headache,  the  bruise  and  the  headache  may 
be  called  joint  effects  of  the  blow.  These  joint  effects 
may  be,  as  it  were,  in  different  degrees  of  descent  from 
the  same  cause.  Thus,  if  the  headache  incapacitates  me 
for  work,  my  incapacity  for  work  and  the  bruise  on  my 
forehead  will  be  joint  effects,  but  in  different  degrees  of 
descent  from  the  original  cause. 

Any  phenomena  which  are  connected,  either  as  cause 
and  effect,  and  that  either  immediately  or  remotely,  or  as 
joint  effects,  and  that  either  in  the  same  or  in  different 
degrees  of  descent  from  the  same  cause,  may  be  spoken 
of  as  being  causally  connected^  or  as  causal  relations^  or 
as  being  related  to  one  another  through  some  fact  of 
causation. 

I  now   proceed   to   the   statement   of  the    Inductive 
Methods. 


*  See  Grove's  Correlation  of  Physical  Forces,  Concluding  Remarks. 
What  Sir  \V.  Grove  calls  *  Force '  would  now  be  denominated 
*  Energy,'  and  the  doctrine  of  the  *  Correlation  of  Physical  Forces  * 
would  be  subsumed  under  that  of  the  *  Conservation  of  Energy.' 


i 


130 


INDUCTIVE  METHODS. 
METHOD   OF   AGREEMENT. 


canon". 
If  two  or  more  instances  of  the  phenomenon  under  investi- 
gation have  only  one  other  circumstance  in  commotio  that 
circumstance  may  be  regarded^  with  more  or  less  of  proba- 
bility^ as  the  cause  (or  effect)  of  the  given  phenomenon,  or,  at 
leasts  as  connected  with  it  through  some  fact  of  causation. 

AVherever  the  phenomenon  a  is  found,  we  observe  that 
h  is  found,  either  invariably  or  frequently  ',  in  conjunction 
with  it.  This  fact  leads  us  to  suspect  that  there  is  some 
causal  connexion  between  them.  On  what  grounds, 
and  under  what  circumstances,  are  we  justified  in  drawing 
such  an  inference  ?  And  what  is  the  particular  character 
of  the  inference  which  we  are  justified  in  drawing?  The 
answer  to  these  questions  involves  many  difficulties,  of 
which  I  shall  now  attempt  to  offer  a  solution. 

When  antecedents  and  consequents  are  discriminated 
in  this  discussion,  antecedents  will  be  represented  by 
Roman  capitals,  A,  B,  C,  &c.,  and  consequents  by  Greek 
characters,  a,  /3,  y,  &:c.  When  circumstances  are  not 
distinguished  as  antecedents  and  consequents,  I  shall 
employ  the  small  Roman  letters,  a,  b,  c,  &c. 

•  The  statement  of  the  Canons  is  taken,  with  some  moclificalions, 
from  Mr.  Mill's  logic.  The  authorities  for  the  various  examples, 
when  these  are  not  of  a  familiar  character,  are  cited  at  the  foot  of  the 
l»age. 

■^  I  add  *  or  frequently,'  as  it  is  not  necessary  that  the  conjunction 
should  be  invariable.  The  student  need  not,  however,  at  present 
tiouble  himself  with  this  distinction,  which  will  be  fully  explained 
below,     See  pp.  137-J^,  145-7. 


1 


METHOD   OF  AGREEMENT, 


131 


Now,  suppose  that  we  have  A  B  followed  by  a  ^,  and 
A  C  by  a  y;  it  might,  at  first  sight,  appear  that  A  must 
be  the  cause  of  o,  or,  if  we  were  attempting  to  ascertain 
the  effect  of  a  given  cause  (which,  however,  is  a  much 
rarer  application  of  this  methods,  that  n  must  be  the 
effect  of  A.  And  there  is  much  plausibility  in  this  sup- 
position, for,  provided  that  all  the  other  circumstances 
remain  the  same,  whatever  can,  in  any  given  instance,  be 
excluded,  or,  to  use  the  technical  term,  eli?ninated  without 
j^rejudice  to  a  phenomenon,  cannot  have  any  influence  on 
it  in  the  way  of  causation,  nor,  making  the  same  proviso, 
can  an  effect  which  disappears  be  due  to  a  cause  which 
continues  to  operate.  Thus,  \i  we  were  attempting  to 
find  the  cause  of  a  given  effect  o,  it  might  be  argued 
that  B  cannot  be  its  cause,  for  it  is  absent  in  one  of  the 
cases  where  a  is  present,  and  similarly  of  C ;  but  that 
ii  must  be  due  to  some  cause ;  and,  consequently,  it  is 
due  to  A,  the  only  antecedent  remaining.  Or,  if  we 
were  attempting  to  find  the  effect  of  a  given  cause  A, 
it  might  be  argued  that  /3  cannot  be  its  effect,  for  it  is 
absent  in  one  of  the  cases  where  A  is  present,  and  simi- 
larly of  y ;  but  that,  as  a  has  been  permanently  present, 
A  must  be  its  cause.  If  it  were  not  for  the  fact  that  the 
same  event  may  be  due  to  a  great  number  of  distinct 
causes  (as  is  exemplified  in  the  familiar  cases  of  motion, 
death,  disease,  &:c.),  this  reasoning  would  be  perfectly 
just.  Now  it  will  be  observed  that,  when  B  was  re- 
moved, it  was  replaced  by  C.  It  is,  therefore,  conceivable 
that  a  may  have  been  due  to  B  in  the  first  instance,  and 

K    2 


132 


INDUCTIVE  METHODS, 


to  C  in  the  second,  it  being,  of  course,  in  each  case,  only 
a  portion  of  the  effect,  the  remaining  portions  being  re- 
spectively i3,  7,  and  A  having  been  throughout  inoperative. 
This  consideration,  it  is  plain,  vitiates  the  reasoning, 
whether  we  are  attempting  to  discover  the  effect  of  a 
given  cause  or  the  cause  of  a  given  effect.  Thus,  suppose 
that  there  are  two  distinct  drugs,  either  of  which  is  potent 
to  remove  a  given  disease,  and  that,  in  administering 
each  of  them,  we  mix  it  with  some  perfectly  inert  sub- 
stance, which  is  the  same  in  each  case ;  if  the  principles 
of  the  above  reasoning  were  correct,  and  we  were  justified 
in  neglecting  to  take  account  of  what  may  be  called  the 
Plurality  of  Causes,  we  should  be  at  liberty  to  argue  (if 
we  were  seeking  the  cause  of  a  given  effect)  that  the 
restoration  of  the  patients  to  health  was,  in  each  case, 
due  to  the  inert  substance,  or  (if  we  were  seeking  the 
effect  of  a  given  cause)  that  the  inert  substance  was  the 
cause  of  their  restoration  to  health. 

But,  if  the  Method  of  Agreement  is  open  to  so  serious 
an  objection,  it  may  be  asked  on  what  grounds  is  it 
recognised  as  an  Inductive  Method  ?  The  answer  is 
that,  by  the  multiplication  and  variation  of  instances, 
the  possible  error  due  to  the  Plurality  of  Causes  may 
be  rendered  less  and  less  probable,  till,  at  last,  for  all 
practical  purposes,  it  may  be  regarded  as  having  disap- 
peared. Thus,  if  to  the  instances  A  B,  a/3 ;  A  C,  ay  ;  we 
can  add  A  D,  «8 ;  A  E,  af,  &c.  &:c. ;  it  is  plain  that  we 
may,  at  each  step,  be  very  considerably  diminishing  the 
possibility  of  an   error   in   our   reasoning,  and,  after  a 


I 


METHOD   OF  AGREEMENT, 


133 


certain  number  of  instances,  may  be  justified  in  feeling 
morally  certain  that  we  have  avoided  it.  It  is  not  likely 
that,  in  a  number  of  instar^ces,  each  agreeing  in  some 
one  circumstance  (besides  the  phenomenon  which  is 
being  investigated)  but  differing  as  widely  as  possible  in 
all  other  circumstances,  the  same  event  should  in  each 
case,  or  in  a  majority  of  cases,  or  in  even  a  great  number 
of  cases,  be  due  to  different  causes.  The  chance  of  an 
inert  substance  being  successively  mixed  with  two  potent 
drugs,  and  of  the  effects  which  are  really  due  to  them 
being  erroneously  ascribed  to  it,  is,  in  the  present  state 
of  medical  science,  but  a  very  slight  one ;  but  the  prob- 
ability is  obviously  considerably  diminished,  if  instead 
of  two  such  errors  we  suppose  three,  instead  of  three  we 
suppose  four,  and  so  on. 

For  the  sake  of  simplicity,  I  have  assumed  groups  of 
two  antecedents  and  two  consequents  (A  B,  a^ ;  A  C, 
ay ;  ^d.  &c.),  but  it  is  extremely  seldom  that  we  find  in 
nature  combinations  so  simple.  We  have  usually  a  vast 
mass  of  antecedents  and  a  vast  mass  of  consequents 
(or,  to  state  the  same  proposition  in  more  scientific  lan- 
guage, a  vast  mass  of  antecedents  all,  or  most  of  them, 
contributing  to  a  complex  effect),  and  hence  it  often 
becomes  a  matter  of  extreme  difficulty  to  discover  a 
collection  of  instances  which,  presenting  the  phenomenon 
in  question,  agree  in  only  one  other  circumstance  or  even 
in  a  small  number  of  other  circumstances.  The  dififi- 
culty,  therefore,  of  rigidly  satisfying  the  requirements  of 
the  Method  must  be  added  to  what  Mr.  Mill  calls  its 


134 


INDUCTIVE  METHODS, 


characteristic  imperfection^  namely,  the  uncertainty  at- 
taching to  its  conclusions  from  the  consideration  of 
the  Plurality  of  Causes. 

But  there  is  still  a  third  difficulty  incident  to  the 
Method  of  Agreement,  which  however  is,  in  a  majority 
of  cases,  of  a  theoretical  rather  than  a  practical  nature. 
If  we  insisted  literally  on  the  fulfilment  of  the  condition 
that  the  instances  presenting  the  given  phenomenon 
should  have  only  one  other  circumstance  in  common,  it 
would  be  simply  impossible  to  find  such  instances.  All 
instances  will  be  found  to  agree  in  a  number  of  circum- 
stances which  are  immaterial  to  the  point  under  inves- 
tigation. Thus,  if  we  are  enquiring  into  the  properties 
of  a  group  of  external  objects,  they  will  all  agree  in  the 
fact  that  they  are  subject  to  the  action  of  gravity,  and 
probably  also  in  the  facts  that  they  are  surrounded  by 
atmospheric  air  and  exposed  to  the  light  of  the  sun  ;  but, 
if  these  facts  do  not  affect  the  subject  of  our  enquiry,  we 
may  pass  them  over  as  if  they  had  no  existence.  When, 
therefore,  we  employ  the  expression  '  only  one  circum- 
stance in  common,'  we  must  be  understood  to  mean 
*only  one  material  circumstance,'  and  to  exclude  all 
circumstances  which  a  wide  experience  or  previous  in- 
ductions have  shown  to  be  immaterial  to  the  question 
before  us.  It  need  hardly  be  added  that,  in  forming 
this  judgment  as  to  the  material  or  immaterial  character  of 
the  circumstances,  the  greatest  caution  is  often  required. 

But,  suppose  we  have  ascertained  (when  enquiring 
into  the  cause  of  a  given  effect)  that  the  instances  agree 


^1 


METHOD    OF  AGREEMENT, 


-^2^:1 


in  only  one  antecedent  (or  rather  one  tnaterial  ante- 
cedent), namely  A,  and  that  we  have  so  multiplied  and 
varied  the  instances  as  to  have  satisfied  ourselves  that 
we  have  excluded  the  possibility  of  a  Plurality  of  Causes, 
are  we  justified  in  drawing  the  inference  that  A  is  the 
cause  of  a  ?  We  are  so  justified,  for  a  must  be  due  to 
something  which  went  before  it,  and,  as  it  has  been 
shown  that  it  is  not  due  to  any  of  the  other  antecedents, 
it  must  be  due  to  A.  Similarly,  if  our  object  be  to 
enquire  into  the  effect  of  a  given  cause  A,  we  are 
justified,  if  we  discover  a  consequent  a,  of  which  we 
can  assure  ourselves  that  it  is  not  due  to  any  of  the 
other  antecedents,  in  regarding  it  as  the  effect  of  A. 

Hitherto,  we  have  supposed  the  antecedents  and  con- 
sequents to  be  discriminated.  But,  suppose  that  we  have 
a  number  of  phenomena  a  b  c  d  e,  a  d  e  f  g,  &c.,  in  which 
we  cannot  discriminate  them,  how  will  the  conclusions 
of  the  Method  of  Agreement  be  affected  ?  There  will,  as 
in  the  former  cases,  obviously  be  the  difficulties  arising 
from  Plurality  of  Causes,  and  the  complexity  of  the 
phenomena.  Supposing,  however,  these  to  be  overcome, 
and  two  circumstances  only,  a  and  b,  to  have  been  ascer- 
tained to  be  common  to  all  the  instances,  what  conclusion 
shall  we  be  justified  in  drawing  with  reference  to  the 
connexion  between  a  and  b?  It  is  only  reasonable 
to  suppose  that  they  must  be  causally  connected  in 
some  way,  else  their  connexion  would  be  a  mere  casual 
coincidence  :  a  supposition  which  we  assume  to  have 
been  excluded  by  the  number  and   variety   of  the  in- 


1^6 


INDUCTIVE   METHODS, 


Stances  examined.  But  they  need  not  necessarily  stand 
to  each  other  in  the  relation  of  cause  and  effect,  for  they 
may  be  common  effects  (in  the  same,  or  in  different  de- 
grees of  descent)  of  some  cause  which  has  itself  ceased 
to  operate.  In  social  and  physiological  phenomena  this 
is  frequently  the  case.  A  disease  will  leave  effects  behind 
it  which  will  continue  to  co-exist  for  years  after  the  disease 
itself  has  passed  away,  and  which,  though  not  standing 
to  each  other  in  the  relation  of  cause  and  effect,  are  thus 
causally  connected.  The  social  condition  of  any  old 
country  is,  to  a  great  extent,  an  aggregate  of  such  effects, 
the  original  cause  or  causes  of  which  have  long  ceased 
to  have  any  existence. 

It  should  be  noticed  that  the  Method  of  Agreement  is 
mainly,  though  not  exclusively,  a  Method  of  Observation 
rather  than  of  Experiment,  and  that  it  is  applied  far  more 
frequently  for  the  purpose  of  enquiring  into  the  causes  of 
given  effects  than  into  the  effects  of  given  causes.  The 
reason  of  this  peculiarity  is  that  in  trying  an  experiment, 
or  in  enquiring  into  the  effect  of  a  given  cause,  we  are 
generally  able  to  employ  one  of  the  other  Methods, 
which,  as  will  be  seen  hereafter,  are  not  exposed  to  the 
same  diflficulties  as  the  Method  of  Agreement. 

It  should  also  be  noticed  that  where,  after  a  careful 
elimination  and  an  examination  of  a  sufficiently  large 
number  of  instances,  we  have,  instead  of  two,  some  three, 
four,  or  more  circumstances  common  to  all  the  instances, 
we  may,  with  much  probability,  regard  them  all,  unless 
we  know  or  suspect  any  of  them  to  be  immaterial  cir- 


METIIOD   OF  AGREEMENT. 


-^zi 


cumstances,  as  being  causally  connected.  If  the  common 
circumstances  be  a,  b,  c,  d,  this  is  all  that  we  can  infer. 
But,  if  they  be  A,  B,  C,  o,  we  may  infer  that  the  cause 
of  n  is  certainly  either  A  or  B  or  C,  or  some  two  of  them 
acting  jointly,  or  all  acting  together,  while  those  common 
antecedents,  which  do  not  either  constitute  or  contribute 
to  the  cause,  probably  stand  in  some  causal  relation  to 
it,  and  consequently  to  its  effect  a.  Similar  conclusions 
may  be  drawn,  if  the  common  circumstances  left  after 
elimination  be  A,  o,  /S,  y.  Thus,  for  instance,  o,  i3,  y 
might  all  be  joint  effects  of  A,  or  a  might  be  its  im- 
mediate effect,  and  3,  y  effects  of  «,  and  so  on. 

It  is  perhaps  not  superfluous  to  remind  the  student 
that,  in  the  application  of  this  Method,  he  should  be 
peculiarly  careful  not  to  overlook  any  instance  in  which 
the  given  phenomenon  is  unaccompanied  by  the  other 
circumstance.  Such  an  instance  should  at  once  lead  him 
to  suspect  that  some  third  common  circumstance,  which 
may  be  the  true  cause  (or  effect)  of  the  given  phenomenon, 
has  escaped  his  attention,  but  this,  if  it  be  the  case,  does 
not  necessarily  vitiate  his  conclusion.  If  the  given  phe- 
nomenon be  the  consequent,  and  this  other  circumstance 
the  antecedent,  such  an  instance  may  only  point  to  some 
other  and  independent  cause  of  the  phenomenon  in  ad- 
dition to  the  cause  he  supposes  himself  to  have  ascer- 
tained. If,  on  the  other  hand,  the  given  phenomenon 
be  the  antecedent,  and  this  other  circumstance  the  con- 
sequent, such  an  instance  may  only  point  to  a  counter- 
acting cause  which,  in  this  exceptional  case,  frustrates 


138 


INDUCTIVE  METHODS, 


the  supposed  effect.  The  only  condition  essential  to 
an  application  of  the  Method  of  Agreement  is  that 
the  cases  on  which  the  inference  is  founded  shall  pre- 
sent only  two  circumstances  in  common.  It  is  not 
necessary  that  these  circumstances  should  invariably  be 
found  in  conjunction,  provided  that  in  the  cases  where 
they  are  found  in  conjunction  no  other  common  cir- 
cumstance can  be  detected.  I  shall  recur  to  this  subject 
below  *. 

In  the  statement  of  the  Canon,  I  have  thought  it 
desirable  to  introduce  the  expression  *  with  more  or  less 
of  probability,'  in  order  to  show  that,  under  no  circum- 
stances, does  an  inference  drawn  in  accordance  with  the 
Method  of  Agreement  attain  to  absolute  and  formal  cer- 
tainty, though,  as  we  have  seen,  it  may  attain  to  moral 
certainty. 

As  familiar  examples  of  the  employment  of  the  Method 
of  Agreement,  the  following  may  be  adduced  : — 

After  taking  a  particular  kind  of  food,  whatever  else  I 
may  eat  or  drink,  and  however  various  my  general  state  of 
health,  the  temperature  of  the  air,  the  climate  in  which  I 
am  living,  and  my  divers  other  surroundings,  I  am  invari- 
ably ill ;  I  am  justified  in  regarding  the  food  as  the  probable 
cause  of  my  illness,  and  avoid  it  accordingly.  This  ex- 
ample furnishes  a  good  illustration  both  of  the  difficulties 
and  of  the  possible  cogency  of  the  Method  of  Agree- 
ment. What  made  me  ill  on  each  of  two,  three,  or  four 
occasions,  may  have  been  some  viand  different  from  the 

"  See  pp.  145-7. 


METHOD   OF  AGREEMENT, 


139 


one  in  question,  but  it  is  very  unlikely,  if  the  number 
of  occasions  on  which  the  inference  is  based  be  con- 
siderable, that  it  has  been  a  different  viand  on  each  of 
them. 

I  find  that  a  certain  plant  always  grows  luxuriantly 
on  a  particular  kind  of  soil ;  if  my  experience  of  the 
other  conditions  be  sufficiently  various,  I  am  justified  in 
concluding  that  the  soil  probably  possesses  certain  chemi- 
cal constituents  which  are  peculiarly  favourable  to  the 
production  of  the  plant. 

Trade  is  observed  to  be  in  a  languishing  condition 
wherever  there  exist  certain  restrictions,  such  as  high 
duties,  difficulties  thrown  in  the  way  of  landing  or  loco- 
motion, &c. ;  if  it  could  be  ascertained  that  these  countries 
agreed  in  no  other  respect  which  could  influence  the 
condition  of  trade,  except  in  being  subject  to  these 
restrictions,  it  might  be  inferred  with  considerable  proba- 
bility that  the  commercial  depression  was  due  to  the 
restrictions  as  a  cause. 

In  all  these  cases,  it  will  be  seen  that  the  great  diffi- 
culty consists  in  ascertaining  that  the  supposed  cause 
is  the  only  circumstance,  or  the  only  material  circum- 
stance, which,  in  addition  to  the  phenomenon  itself,  the 
various  instances  possess  in  common. 

I  now  append  a  few  instances  of  a  less  familiar  nature : — 

The  occurrence  of  Aurora  Borealis  has,  under  me- 
teorological conditions  of  very  different  character,  been 
invariably  found  to  be  accompanied  by  considerable 
magnetic  disturbances.     It  is  rightly  inferred  that  there 


140 


INDUCTIVE  METHODS, 


is  some  causal  connexion  between  magnetic  disturbance 
and  the  occurrence  of  the  Aurora  Boreahs. 

It  has  been  observed  uniformly,  and  under  a  variety  of 
circumstances,  that,  wherever  an  indiscriminate  system 
of  almsgiving  has  prevailed,  the  population  has,  sooner 
or  later,  become  indolent  and  pauperised.  This  fact 
may  be  noticed  especially  in  the  neighbourhood  of  large 
monasteries,  in  parishes  where  large  sums  of  money 
are  distributed  in  the  shape  of  *  doles,'  in  places  which 
are  the  residence  of  rich  and  charitable  but  injudicious 
persons,  and  the  like.  The  reason  is  not  difficult  to 
discover.  The  unfortunate  recipients  of  the  charity  are 
left  without  the  ordinary  motives  to  exertion,  and  con- 
sequently, when  the  abnormal  supply  ceases,  or  becomes 
too  small  for  the  wants  of  an  increased  population,  being 
without  self-reliance  or  any  special  skill,  they  have  no 
resource  but  beggary. 

After  a  variety  of  experiments  on  substances  of  the 
most  different  kinds,  and  under  the  most  different  cir- 
cumstances, it  has  been  found  that,  as  a  body  passes 
from  a  lower  degree  of  temperature  to  a  higher,  it  in- 
variably undergoes  a  change  of  volume,  though  that 
change  may  not  always  be  in  the  same  direction,  it  being, 
in  the  great  majority  of  cases,  in  the  direction  of  expan- 
sion, but,  occasionally,  in  that  of  contraction.  Hence  it  has 
been  inferred  that  change  of  volume  is  an  invariable  effect 
of  change  of  temperature  (it  being  understood,  of  course, 
that  pressure  and  other  circumstances,  as,  for  instance, 
the  chemical  condition  of  the  body,  remain  the  same). 


METHOD   OF  AGREEMENT, 


141 


It  has  been  supposed  by  some  writers  on  physics  that  we 
may  go  further  than  this  conclusion,  and  state  that 
augmentation  of  temperature  is  invariably  followed  by 
augmentation  of  volume,  and  diminution  of  temperature 
by  diminution  of  volume,  the  exceptions  of  water®  as 
well  as  of  bismuth  and  of  the  casting-metals  generally 
(which  suddenly  expand  at  the  moment  of  solidification) 
being  explained  as  anomalies  due  to  some  interfering 
cause.  We  are,  however,  at  present  so  little  acquainted 
with  the  intimate  constitution  of  bodies,  that  it  might  be 
rash  to  state  the  proposition  in  this  form,  and,  stated  as 
above,  it  is  open  to  no  exception  ^°. 

*  Water  follows  the  general  rule,  and  continues  to  contract  in  bulk 
as  its  temperature  is  lowered,  till  it  reaches  about  39°  Fahrenheit  or 
4°  Centigrade,  when  it  begins  to  expand,  and  continues  to  do  so  till 
after  its  conversion  into  ice,  so  that  a  given  weight  of  water  at  the 
temperature  ,.say)  of  37'^,  or  when  fiozen,  occupies  more  space  than 
it  occupied  at  (sajO  the  temperature  of  40°.  This  anomaly  is  some- 
what boldly  explained  by  Sir  W.  Grove  as  due  to  the  setting  in  o 
the  process  of  crystallization,  which  he  supposes  to  begin  at  39°,  and 
to  interfere  with  the  ordinary  law  of  contraction  and  expansion. 
(See  Grove's  Correlation  of  Physical  Forces,  fifth  ed.  p.  58,  &c.) 

*"  I  adduce  this  instance  as  an  example  of  the  Method  of  Agree- 
ment rather  than  of  the  Method  of  Concomitant  Variations,  because 
the  argument,  as  here  stated,  rests  rather  upon  the  variation  of 
circumstances  and  the  great  diversity  of  bodies  in  which  the  law 
is  found  to  hold  good,  than  upon  the  relation  between  the  various 
degrees  of  expansion  or  contraction  and  the  various  degrees  of 
temperature  in  the  same  body.  Had  the  stress  been  laid  upon  the 
latter  consideration,  the  argument  would  undoubtedly  have  been  an 
instance  of  the  Method  of  Concomitant  Variations. 

It  frequently  happens,  in  fact,  that  two  or  more  Methods  are 
combined  in  the  same  proof.  In  the  present  instance,  as  will  be 
seen  below,  the  argument  as  applied  to  each  particular  kind  of  body 


142 


INDUCTIVE  METHODS, 


The  following  example,  which  also  illustrates  the 
caution  necessary  to  be  observed  in  framing  a  general 
proposition,  is  extracted  from  Sir  John  Herschel's  Dis- 
course on  the  Study  of  Natural  Philosophy'^^ : — 

*  A  great  number  of  transparent  substances,  when  exposed, 
in  a  certain  particular  manner,  to  a  beam  of  light  which  has 
been  prepared  by  undergoing  certain  reflexions  or  refractions 
(and  has  thereby  acquired  peculiar  properties,  and  is  said 
to  be  '''•polarized^''),  exhibit  very  vivid  and  beautiful  colours, 
disposed  in  streaks,  bands,  &c.  of  great  regularity,  which  seem 
to  arise  within  the  substance,  and  which,  from  a  certain 
regular  succession  observed  in  their  appearance,  are  called 
"  periodical  colours."  Among  the  substances  which  exhibit 
these  periodical  colours  occur  a  great  variety  of  transparent 
solids,  but  no  fluids  and  no  opaque  solids.  Here,  then,  there 
seems  to  be  sufficient  community  of  nature  to  enable  us  to 
use  a  general  term,  and  to  state  the  proposition  as  a  law, 
viz.  transparent  solids  exhibit  periodical  colours  by  exposure 
to  polarized  light.  However,  this,  though  true  of  many,  does 
not  apply  to  all  transparent  solids,  and  therefore  we  cannot 
state  it  as  a  general  truth  or  law  of  nature  in  this  form ; 
although  the  reverse  proposition,  that  all  solids  which  exhibit 

(mercuiy,  for  instance  is  an  argument  based  on  the  Method  of 
Concomitant  Variations ;  but  when  we  proceed  to  extend  the  experi- 
ment to  other  bodies,  and  then  argue  from  the  variety  of  the  bodies 
examined  that  a  body,  in  passing  from  one  degree  of  temperature  to 
another,  invariably  undergoes  a  change  of  volume,  it  appears  to  me 
that  we  are  no  longer  employing  the  Method  of  Concomitant  Varia- 
tions but  the  Method  of  Agreement.  It  must  Jt>e  home  in  mind  that 
the  object  of  our  enquiry  is  not  strictly  the  effects  of  heat  (for  the 
total  effects  of  heat,  inasmuch  as  we  cannot  wholly  exhaust  any  body 
of  its  heat,  must  be  unknown  to  us),  but  the  effects  of  a  change  of 
temperature. 


METHOD   OF  AGREEMENT 


M3 


such  colours  in  such  circumstances  are  transpareiit^  would 
be  correct  and  general.  It  becomes  necessary,  then,  to  make 
a  Hst  of  those  to  which  it  does  apply  ;  and  thus  a  great 
number  of  substances  of  all  kinds  become  grouped  together 
in  a  class  linked  by  this  common  property.  If  we  examine 
the  individuals  of  this  group,  we  find  among  them  the  utmost 
variety  of  colour,  texture,  weight,  hardness,  form,  and  com- 
position ;  so  that,  in  these  respects,  we  seem  to  have  fallen 
upon  an  assemblage  of  contraries.  But,  when  we  come  to 
examine  them  closely  in  all  their  properties,  we  find  they  have 
all  one  point  of  agreement,  in  the  property  of  double  refrac- 
tion, and  therefore  we  may  describe  them  all  truly  as  doubly 
refracting  substances.  We  may,  therefore,  state  the  fact  in 
the  form,  **  Doubly  refracting  substances  exhibit  periodical 
colours  by  exposure  to  polarized  light ; "  and  in  this  form  it 
is  found,  on  further  examination,  to  be  true,  not  only  for  those 
particular  instances  which  we  had  in  view  when  we  first  pro- 
pounded it,  but  in  all  cases  which  have  since  occurred  on 
further  enquiry,  without  a  single  exception ;  so  that  the 
proposition  is  general,  and  entitled  to  be  regarded  as  a  law 
of  nature.* 


The  experiments  by  which  Dr.  Wells  '^  established  his 
Theory  of  Dew  afford  a  remarkable  example  of  the 
Method  of  Agreement.  By  employing  various  objects 
of  different  material  under  a  variety  of  circumstances, 

"  Dr.  Wells'  Memoir  on  the  Theory  of  Dew,  which  had  become- 
very  scarce,  was  reprinted  by  Longmans  and  Co.  in  1866.  It  is  very 
brief,  and  well  deserves  to  be  carefully  read  by  every  student  of 
scientific  method.  Sir  John  Herschel  {Natural  Philosophy,  §  168 
speaks  of  the  speculation  as  *  one  of  the  most  beautiful  specimens ' 
he  can  call  to  mind  *  of  inductive  experimental  enquiry  lying  within 
a  moderate  compass.*  Mr.  Mill  also  employs  it  as  one  of  bis 
Miscellaneous  Examples  in  Bk.  III.  ch.  ix.  of  his  Logic, 


144 


INDUCTIVE  METHODS. 


he  showed  that,  whatever  the  texture  of  the  object,  the 
state  of  the  atmosphere,  &c.,  it  is  an  invariable  condition 
of  the  deposition  of  dew  that  the  object  on  which  it  is 
deposited  shall  be  colder  than  the  surrounding  atmo- 
sphere, the  greater  coldness  of  the  object  being  itself 
produced  by  the  radiation  of  heat  from  its  surface. 
This,  to  quote  the  words  of  Sir  John  Herschel,  is  the 
case  not  only  with  '  nocturnal  dew,'  but  with  '  the  analo- 
gous phenomena  of  '  the  mois'.ure  which  bedews  a  cold 
metal  or  stone  when  we  breathe  upon  it ;  that  which 
appears  on  a  glass  of  water  fresh  from  the  well  in  hot 
weather ;  that  which  appears  on  the  inside  of  windows 
when  sudden  rain  or  hail  chills  the  external  air  ;  that 
which  runs  down  our  walls  when,  after  a  long  frosty  a 
warm  moist  thaw  comes  on.' 

It  is  by  the  Method  of  Agreement  that  we  discover  the 
symptoms  of  a  disease,  the  signs  of  a  political  revolution, 
national  characteristics,  the  order  of  superposition  among 
geological  strata,  grammatical  rules,  and  the  like. 

The  first  division  of  Bacon's  insfantiie  solitarice  coin- 
cides with  the  cases  contemplated  in  the  Method  of 
Agreement,  as  the  second  coincides  with  the  cases  con- 
templated in  the  Method  of  Difference.  The  example 
employed  in  the  first  is  so  remarkable  both  in  itself,  and 
as  an  anticipation  of  Newton's  Speculations  on  Colour, 
that  I  may  adduce  it  as  an  additional  instance  of  the 
Method  of  Agreement : — 

'  Exempli  gratia  :  si  fiat  inquisitio  de  natura  colons^ 
insianiiw  so/itarice  sunt  prismata,  gemmae  crystallinoe,  quse 


METHOD   OF  AGREEMENT, 


145 


reddunt  colores,  non  solum  in  se,  sed  exterius  supra 
parietem.  Item  rores,  &c.  Istae  enim  nil  habent  com- 
mune cum  coloribus  fixis  in  floribus,  gemmis  coloratis, 
metallis,  lignis,  &c.  praeter  ipsum  colorem.  Unde  facile 
colligitur,  quod  color  nil  aliud  sit  quam  modificatio  ima- 
ginis  lucis  immissae  et  receptae  :  in  priore  genera,  per 
gradus  di versos  incidentiae  ;  in  posteriore,  per  texturas  et 
schematismos  varios  corporis.  Istae  autem  instantice.  sunt 
solitarice  quatenus  ad  similitudinem  ".' 

In  attempting  to  ascertain  the  cause  of  a  given  effect, 
a,  it  may  happen  that  we  find  a  particular  antecedent, 
A,  frequently,  but  not  invariably,  accompanying  it.  If, 
in  those  cases  which  present  both  a  and  A,  no  other 
common  circumstance  can  be  detected,  we  may  infer 
that  A  is  probably  a  cause  of  a.  I  say  'a  cause,'  for 
the  fact  that  a  may  be  present  without  A  is  a  proof  that 
A  is  not  the  only  cause.  My  meaning  will  be  plain  from 
the  following  example : — 

We  compare  instances  in  which  bodies  are  known  to 
assume  a  crystalline  structure,  but  which  have  no  other 
point  of  agreement ;  in  the  great  majority  of  instances, 
though  not  in  all,  we  find  that  these  bodies  have  assumed 
their  crystalline  structure  during  the  process  of  solidifica- 
tion from  a  fluid  state,  either  gaseous  or  liquid,  and,  so 
far  as  we  can  ascertain,  these  cases  have  no  other  cir- 
cumstance in  common.  From  these  facts  it  may  be 
reasonably  inferred   that   the   passage  from  a  fluid   to 


"  Novum  Organum,  Lib.  II.  aph.  xxii. 


146 


INDUCTIVE  METHODS. 


a  solid  state  is  a  cause,  though  not  the  only  cause,  of 
crystallization  ^*. 

Again,  when  A  is  frequently,  though  not  invariably, 
followed  by  o,  and  there  is,  so  far  as  we  can  ascertain, 
no  other  common  antecedent,  we  are  justified  in  sus- 
pecting that  A  is  a  cause  of  o,  and  that,  in  the  cases 
where  a  does  not  occur,  the  operation  of  A  is  counter- 
acted by  some  other  cause.  If,  for  example,  a  certain 
occupation  or  mode  of  living  is  found  to  be  usually, 
though  not  invariably,  attended  by  a  particular  form  of 
disease,  we  seem  to  be  justified  in  regarding  this  occupation 
or  mode  of  living  as  a  cause  of  the  disease,  and  in  explain- 
ing the  few  cases  in  which  the  disease  does  not  occur  as 
due  to  exceptional  and  counteracting  circumstances. 

Similarly,  when  a  and  b  are  found  in  frequent,  though 
not   invariable,  conjunction  ^^,  and,  in  the  cases  where 

"  This  example  is  adopted,  with  considerable  modifications,  from 
one  which  occurs  in  Mr.  Mill's  Logic,  Bk.  III.  ch.  viii.  §1.  1  am 
indebted  to  Sir  John  Ilerschel  for  pointing  out  to  me  that  Mr.  Mill's 
example  (which  I  had  originally  adopted  as  it  stood)  is  too  broadly 
stated.  *  The  solidification  of  a  i^ubstance  from  a  liquid  [it  should 
be  fluid]  state  '  is  not  *  an  invariable,'  but  only  an  usual  *  antecedent 
of  its  crystallization.'  The  reader  will  find  several  exceptions 
noticed  in  Watts'  Dictionary  of  Chemistry^  art.  Crystallization. 

•*  The  invarinble  conjunction  of  two  phenomena,  when  the  pre- 
sence of  the  one  implies  the  presence  of  the  other,  and  the  absence 
of  the  one  the  absence  of  the  other,  is  a  case  falling  under  the 
Double  Method  of  Agreement,  to  be  explained  presently  ;  but  those 
cases,  in  which  we  simply  know  that  a  given  phenomenon  is  invari- 
ably preceded  or  invariably  followed  by  another,  fall  under  the 
Method  of  Agreement  just  discussed.  If  a  given  phenomenon  is, 
so  far  as  we  know,  invariably  preceded  by  another,  this  fact  justifies 


METHOD   OF  AGREEMENT, 


147 


they  are  found  together,  there  occurs,  so  far  as  we  can 
ascertain,  no  other  common  circumstance,  w-e  are  justified 
in  suspecting  that  there  exists  some  causal  connexion 
between  them. 

The  student,  who  is  acquainted  with  the  science  of 
Medicine,  will  find  a  good  illustration  of  the  extreme 
difficulty  attending  the  application  of  the  Method  of 
Agreement,  as  well  as  of  the  Joint  Method  of  Agreement 
and  Difference  (to  be  noticed  presently),  in  the  disputes 
which  still  occur  as  to  the  cause  of  the  mental  disease 
which  is  known  as  Atactic  Aphasia,  that  is,  the  condition 
in  which,  with  reference  to  certain  sounds,  the  patient 
has  lost  the  power  of  co-ordinating  the  muscles  of  speech. 
The  French  physiologist,  M.  Broca,  laid  down  the  posi- 
tion that  this  disease  is  invariably  due  to  a  lesion  of  the 
third  frontal  convolution  of  the  left  hemisphere  of  the 
brain,  the  disease  being  invariably  attended  by  the  specific 
lesion,  and  the  lesion  never  occurring  without  the  disease. 
His  followers  maintain  that  the  instances  are  decisive  in 
favour  of  this  theory,  while  the  apparent  exceptions  admit 

us  in  suspecting  (though  it  docs  not  prove)  that  the  antecedent  is 
not  only  a  cause,  but  the  only  cause,  of  the  given  phenomenon. 
Such  a  conclusion  can  only  be  proved  (even  approximately)  by  the 
Double  Method  of  Agreement.  It  is,  however,  as  already  pointed 
out,  not  in  the  invariableness  of  the  conjunction,  but  in  the  fact  that 
the  instances  examined  present,  so  far  as  we  can  ascertain,  only  two 
phenomena  in  common,  that  the  cogency  of  the  Method  of  Agree- 
ment consists.  But  of  this  fact  invariableness  of  antecedence  (or  of 
consequence)  furnishes  one  of  the  strongest  proofs,  inasmuch  as  such 
invariableness  implies  a  very  wide  variation  of  circumstances  ;  hence 
the  stress  laid  upon  it  in  some  of  the  examples  adduced  above. 

L    2 


148 


INDUCTIVE  METHODS, 


of  a  satisfactory  explanation  ;  his  opponents,  on  the 
other  hand,  assert  that  there  are  well-established  cases 
both  of  atactic  aphasia  without  the  specific  lesion,  and 
of  the  lesion  without  aphasia  ^^ 

METHOD    OF    DIFFERENCE. 

CANON. 

If  an  instance  in  7vhich  the  phenomenon  under  investi- 
gation occurs^  and  an  instance  in  which  it  does  not  occur, 
have  every  circumstance  in  common  save  one,  that  one  oc- 
curring only  in  the  for?ner ;  the  circu instance  in  which 
alone  the  tivo  instances  differ^  is  the  effect^  or  cause^  or  a 
necessary  part  of  the  cause ^  of  the  phenotnenoti. 

The  circumstances  a,  b,  c  are  found  in  conjunction 
with  d,  e,  f,  and  the  omission  or  disappearance  of  the  cir- 
cumstance a  is  found  to  be  attended  by  the  disappearance 
of  the  circumstance  d.  It  is  inferred  that  a  and  d  are 
so  connected  that  one  is  cause  (or  a  necessary  part  of 
the  cause)  and  the  other  effect.  If,  moreover,  it  can 
be  ascertained  that  a  is  the  antecedent  and  d  the  con- 

*^  See  a  paper  by  Dr.  William  Ogle  in  the  St.  George  s  Hospital 
Reports,  vol.  ii. ;  a  Pnmphlet  Ity  Dr.  P'rederic  Bateman  of  Norwich, 
published  by  J.  E.  Adlard,  Bartholomew  Close,  London,  1868; 
Dr.  Reynolds'  System  of  Medicine.)  vol.  ii.  pp.  442-444  ;  and  various 
reports  of  discussions  published  in  the  Lancet  and  other  medical 
journals.  I  have  to  thank  my  friends,  Professors  Acland  and 
Rolleston,  for  their  kindness  in  supplying  me  with  information  on 
this  interesting  subject,  and  regret  that  my  space  prevents  me  from 
pursuing  it  at  greater  length. 


METHOD   OF  DIFFERENCE. 


149 


sequent,  or  that,  though  there  are  instances  in  which  d 
occurs  without  a,  there  are  no  instances  in  which  a  occurs 
without  d,  we  may  proceed  to  yifer  (in  the  latter  case,  on 
the  ground  that  a  phenomenon  may  have  more  than  one 
cause,  but  that  a  cause,  unless  counteracted  by  some  other 
cause,  must  be  attended  by  its  effect)  that  a  is  the  cause, 
and  d  the  effect.  Similarly,  if  the  circumstances  a,  b,  c 
are  found  in  conjunction  with  d,  e,  f,  and  the  introduction 
of  the  circumstance  x  into  the  former  set  of  phenomena 
is  found  to  be  attended  by  the  appearance  of  the  cir- 
cumstance y  in  the  latter  set  of  phenomena  (so  that  they 
may  be  represented  respectively  as  a,  b,  c,  x  ;  d,  e,  f,  y), 
it  may  be  inferred  that  x  and  y  are  related  as  cause 
and  effect ;  or,  if  x  be  the  antecedent  and  y  the  con- 
sequent, or  the  appearance  of  x  be  invariably  attended 
by  the  appearance  of  y  while  the  appearance  of  y  is 
not  invariably  attended  by  the  appearance  of  x,  that  x 
is  the  cause  and  y  the  effect.  The  reasons  on  which 
the  Canon  rests  are  obvious.  All  other  circumstances 
remaining  the  same,  if  the  introduction  or  omission  of 
any  circumstance  be  followed  by  a  change  in  the  remain- 
ing circumstances,  that  change  must  be  due  to  such 
introduction  or  omission,  as  an  effect  to  a  cause;  or, 
if  two  new  circumstances  enter  simultaneously,  without 
producing  any  other  change  in  the  phenomenon,  these 
two  circumstances  (except  on  the  improbable  suppo- 
sition that  they  are  two  causes  exactly  counteracting  each 
other)  must  be  related  as  cause  and  effect,  though  we 
may  be  unable  to  say  which  of  the  two  is  cause  and 


I50 


INDUCTIVE  METHODS, 


which  effect.  *  The  Method  of  Agreement/  says  Mr. 
Mill,  '  stands  on  the  ground  that  whatever  can  be  eli- 
minated, is  not  connected  with  the  phenomenon  by  any 
law.  The  Method  of  Difference  has  for  its  foundation 
that  whatever  can  not  be  eliminated,  is  connected  with 
the  phenomenon  by  a  law.'  In  the  Method  of  Differ- 
ence, the  instances  agree  in  everything,  except  in  the 
possession  of  two  circumstances  which  are  present  in 
the  one  instance  and  absent  in  the  other.  In  the  Method 
of  Agreement,  the  various  instances  compared  (for  here 
we  generally  require  more  than  two  instances)  agree  in 
nothing,  except  in  the  possession  of  two  circumstances 
which  are  common  to  all  the  instances.  One  Method 
is  called  the  Method  of  Agreement,  because  we  compare 
various  instances  to  see  in  what  they  agree  ;  the  other 
is  called  the  Method  of  Difference,  because  we  compare 
an  instance  in  which  the  phenomenon  occurs  with 
another  in  which  it  does  not  occur,  in  order  to  see  in 
what  they  differ. 

Instances  of  the  Method  of  Difference  are  not  far 
to  seek.  A  piece  of  paper  is  thrown  into  a  stove  ;  we 
have  no  hesitation  in  regarding  its  apparent  consumption 
as  the  effect  of  the  heat  of  the  fire,  for  we  feel  assured 
that  the  sudden  increase  of  temperature  is  the  only  new 
circumstance  to  which  the  piece  of  paper  is  exposed,  and 
that,  therefore,  any  change  in  the  condition  of  the  paper 
must  be  due  to  that  cause.  A  bullet  is  fired  from  a  gun, 
or  a  dose  of  prussic  acid  is  administered,  and  an  animal 
instantly  falls   down  dead.      There  is  no  hesitation  in 


METHOD   OF  DIFFERENCE. 


151 


ascribing  the  death  to  the  gun-shot  wound  or  the  dose 
of  poison.     Nor  is   this  confidence  the   effect   of  any 
wide  experience,  for,   if  it  were  the  first  time  that  we 
had  seen  a  gun  fired  or  a  dose  of  poison  administered, 
we  should  have  no  hesitation   in  ascribing   the  altered 
condition  of  the  animal  to  this  novel  cause ;  we  should 
know  that  there  was  only  one  new  circumstance  operating 
upon  it,  and,  consequently,  that  any  change  in  its  con- 
dition must  be  due  to  that  one  circumstance.  In  all  these 
instances,  there  is  the  introduction  of  a  new  antecedent, 
x,  to  which  the  new  consequent,  y,  must  be  due.     But, 
if  the  omission  of  one  circumstance  be  attended  by  the 
omission  of  another,  we  may  argue  with  equal  confidence. 
I  withdraw  my  hand   from  this   book  which  is  resting 
upon  it,  and  the  book  instantly  falls  to  the  ground  ;  there 
is  no  hesitation  in  referring  the  altered  position  of  the 
book   to   the   withdrawal   of    my   support.      A   man    is 
deprived  of  food,  and  he  dies  ;  we  have  no  hesitation  in 
ascribing  the  disappearance  of  the  phenomenon  we  call 
life  to  the  withdrawal  of  the  means  by  which  it  is  main- 
tained.    In  these  instances,  we  have  certain  antecedents, 
followed    by  certain    consequents,    and,    observing   the 
simultaneous  or  successive   disappearance   of  A  and  a, 
we  have  no  hesitation  in  connecting  the   two  as  cause 

and  effect. 

All  crucial  instances   (instantiae  ^'   crucis,  as  they   are 

■^  '  Inter  prserogativas  instantianim  poncmus  loco  decimo  quarto 
instantias  crucis ;  translate  vocabulo  a  crucibus,  quae,  erectge  in 
l)iviis,  indicant  et  signant  viarum  separationes.     Has  etiam  instantias 


15^ 


INDUCTIVE  METHODS, 


called  by  Bacon)  are  applications  of  the  Method  of  Dif- 
ference. A  crucial  instance  is  some  observation  or  ex- 
periment which  enables  us  at  once  to  decide  between 
two  or  more  rival  hypotheses.  It  will  be  familiar  to 
every  one  in  the  form  of  the  chemical  test,  as  where  we 
apply  an  acid  for  the  purpose  of  determining  the  character 
of  a  metal,  or  a  metal  for  the  purpose  of  detecting  latent 
poison.  According  to  the  metaphor,  there  are  two  or 
more  ways  before  us,  and  the  observation  or  experiment 
acts  as  a  '  guide-post '  (crux)  in  determining  us  which  to 
take.  The  following  beautiful  example  of  a  Crucial 
Instance  is  borrowed  from  Sir  John  Herschel  '*. 

*  A  curious  example  is  given  by  M.  Fresnel,  as  decisive, 
in  his  mind,  of  the  question  between  the  two  great 
opinions  on  the  nature  of  light,  which,  since  the  time  of 

decisoriaSf  GiJudicialeSj  et  in  casibus  nonnullis  instantias  oracttli,  et 
mandati,  appellare  consuevinuis.  Earum  ratio  talis  est.  Cum  in 
inquisitioae  naturai  alicujus,  intellectus  ponitur  tanquam  in  aequili- 
brio,  ut  incertus  sit,  utri  naturarum  e  duabus,  vel  quandoque  pluribus, 
causa  natura'  inquisita:  attribui  aut  assignari  debeat,  propter  com- 
plurium  naturarum  concursum  frequentem  et  ordinarium  ;  instantiit 
crucis  ostenduiit  consortium  unius  ex  naturis  (quoad  naturam  in- 
quisitam)  fidum  et  indissolubilc,  alterius  autem  varium  et  separabile  ; 
unde  terminatur  qusestio,  et  recipitur  natura  ilia  prior  pro  causa, 
missa  altera  et  repudiata.  Itaque  hujusmodi  instantia;  sunt  maximae 
lucis,  et  quasi  ma<;nDe  auctoritatis ;  ita  ut  curriculum  interpretationis 
quandoque  in  illas  desinat,  et  per  illas  perficiatur.  Interdum  autem 
insta>itii€  crucis  ilUv  occurrunt  et  inveniuntur  inter  jampridem 
notatas ;  at  ut  plurimum  novie  sunt,  et  de  industria  atque  ex  com- 
posito  quaesitce  et  applicatoe,  et  diligentia  sedula  ct  acri  tandem 
erutae.' — Novum  Organum,  Lib.  II.  aph.  xxxvi. 

"  Discourse  on  the  Study  of  NaturcU  Philosophy,  §  218. 


METHOD   OF  DIFFERENCE, 


''S?^ 


Newton  and  Huyghens,  have  divided  philosophers  ;' — 
that  is,  between  what  is  called  'the  emission  theory,' 
according  to  which  light  consists  of  actual  particles 
emitted  from  luminous  bodies,  and  what  is  called  'the 
undulatory  theory,'  according  to  which  light  consists  in 
the  vibrations  of  an  elastic  medium  pervading  all  space. 

*  When  two  very  clean  glasses  are  laid  one  on  the  other, 
if  they  be  not  perfectly  flat,  but  one  or  both  in  an  almost  im- 
perceptible degree  convex  or  prominent,  beautiful  and  vivid 
colours  will  be  seen  between  them ;  and  if  these  be  viewed 
through  a  red  glass,  their  appearance  will  be  that  of  alternate 
dark  and  bright  stripes.  These  stripes  are  formed  between 
the  two  surfaces  in  apparent  contact,  as  any  one  may  satisfy 
himself  by  using,  instead  of  a  flat  plate  of  glass  for  the  upper 
one,  a  triangular-shaped  piece,  called  a  prism,  like  a  three- 
cornered  stick,  and  looking  through  the  inclined  side  of  it 
next  the  eye,  by  which  arrangement  the  reflexion  of  light 
from  the  upper  surface  is  prevented  from  intermixing  with 
that  from  the  surfaces  in  contact.  Now,  the  coloured  stripes 
thus  produced  are  explicable  on  both  theories,  and  are  appealed 
to  by  both  as  strong  confirmatory  facts ;  but  there  is  a  dif- 
ference in  one  circumstance  according  as  one  or  the  other 
theory  is  employed  to  explain  them.  In  the  case  of  the 
Huyghenian  doctrine,  the  intervals  between  the  bright  stripes 
ought  to  appear  absolutely  black;  in  the  other,  half  bright, 
when  so  viewed  through  a  prism.  This  curious  case  of  dif- 
ference was  tried  as  soon  as  the  opposing  consequences  of 
the  two  theories  were  noted  by  M.  Fresnel,  and  the  re- 
sult is  stated  by  him  to  be  decisive  in  favour  of  that  theory 
which  makes  light  to  consist  in  the  vibrations  of  an  elastic 
medium  '\' 

'^  Mr.  Mill  {Logic,  Bk.  III.  ch.  xiv.  §  6)  maintains  that  it  does  not 
follow  from  this  experiment  that '  the  phenomena  of  light  are  results 


154 


INDUCTIVE   METHODS. 


METHOD   OF  DIFFERENCE, 


DO 


The  following  is  an  example  of  a  similar  kind.  It 
had  been  determined,  from  theoretical  considerations, 
that,  on  the  assumption  of  the  undulatory  theory,  the 
velocity  of  light  must  be  less  in  the  more  highly  refract- 
ing medium,  while,  according  to  the  emission  theory, 
it  ought  to  be  greater.  When  M.  Foucault  had  invented 
his  apparatus  for  determining  the  velocity  of  light,  it 
became  possible  to  submit  the  question  to  direct  ex- 
jjeriment ;  and  it  was  established  by  himself  and  M. 
Kizeau  that  the  velocity  of  light  is  less  in  water  (the 
more  highly  refracting  medium)  than  in  air,  in  the  in- 
verse proportion  of  the  refractive  indices.  The  result 
is,  therefore,  decisive  in  favour  of  the  undulatory,  or, 
at  least,  against  the  emission  theory  '^ 

There  is  no  science,  perhaps,  in  which  the  Method 
of  Difference  is  so  extensively  used  as  the  science  of 
('hemistry,  and  that  because  chemistry  is  emphatically  a 
science  of  experiment.  Almost  any  chemical  experiment 
will  serve  as  an  instance  of  the  Method  of  Difference. 
Mix,  for  example,  chloride  of  mercury  with  iodide  of 
potassium,  and  the  result  will  be  a  colourless  liquid  at 
the  top  of  the  vessel  with  a  brilliant  red  precipitate  at 

i)f  the  law>^  of  clastic  fluids,  but  at  most  that  they  are  governed  by 
laws  partially  identical  with  these.'  But,  though  the  experiment  may 
not  be  decisive  as  in  favour  of  the  Undulatory  Theory,  it  is  un- 
<ioubtcdly  decisive  as  against  the  Eniissi  m  1  heory.  It  may  be 
necessiry  to  add  that  the  term  '  fluids '  would  now  be  repudiated  by 
those  wl  o  hold  the  Undi  latory  Theory. 

**  SfC    Lloyd's    Wave    Theory  of  light,   3rd  ed.   Arts.  41,   42  ; 
(Janot's  PhysicSy  English  translation,  nth  edition,  Art.  506. 


\ 


the  bottom.     There  can  be  no  hesitation  in  ascribing 
this  result  to  the  mixture  of  the  two  liquids ;  and  two 
similar  experiments  will  enable  us  to  determine  that  the 
chlorine  has  been  set  free  from  the  mercury  and  united 
with  the  potassium,  which  itself  has  been  set  free  from 
the  iodine  with   which   it  was  previously  united,  while 
the  iodine  has  united  with  the  mercury,  the  former  pro- 
ducing chloride  of  potassium  (dissolved  in  the  colourless 
liquid),  the  latter  iodide  of  mercury  (the  red  precipitate). 
The  science  of  Heat  (or,  as  Dr.  Whewell  proposes  to 
call  it,  Thermotics)  also  furnishes  excellent  examples  of 
the  Method  of  Difference.     The  following  instances  are 
adapted   from    Professor    Tyndall's    Heat  a   Mode    of 
Motion  ^'  : — 

'  Here  is  a  brass  tube,  four  inches  long,  and  of  three- 
quarters  of  an  inch  interior  diameter.  It  is  stopped  at  the 
bottom  and  screwed  on  to  a  whirling  table,  by  means  of 
which  the  upright  tube  can  be  caused  to  rotate  very  rapidly. 
These  two  pieces  of  oak  are  united  by  a  hinge,  in  which  are 
two  semicircular  grooves,  intended  to  embrace  the  brass  tube. 
Thus  the  pieces  of  wood  form  a  kind  of  tongs,  the  gentle 
squeezing  of  which  produces  friction  when  the  tube  rotates. 
I  partially  fill  the  tube  with  cold  water,  stop  it  with  a  cork 
to  prevent  the  splashing  out  of  the  liquid,  and  now  put  the 
machine  in  motion.  As  the  action  continues,  the  temperature 
of  the  water  rises,  and  now  the  tube  is  too  hot  to  be  held  in 
the  fingers.  Continuing  the  action  a  little  longer,  the  cork 
is  driven  out  with  explosive  violence,  the  steam  which  follows 
it  producing  by  its  precipitation  a  small  cloud  in  the  atmo- 
sphere.' 

21  Third  Edition,  ch.  i.  §§  14-16. 


J  54 


INDUCTIVE  METHODS. 


METHOD   OF  DIFFERENCE, 


1"  f 


The  following  is  an  example  of  a  similar  kind.  It 
had  been  determined,  from  theoretical  considerations, 
that,  on  the  assumption  of  the  undulatory  theory,  the 
velocity  of  light  must  be  less  in  the  more  highly  refract- 
ing medium,  while,  according  to  the  emission  theory, 
it  ought  to  be  greater.  When  M.  Foucault  had  invented 
his  apparatus  for  determining  the  velocity  of  light,  it 
became  possible  to  submit  the  question  to  direct  ex- 
jjeriment ;  and  it  was  established  by  himself  and  M. 
Fizeau  that  the  velocity  of  light  is  less  in  water  (the 
more  highly  refracting  medium)  than  in  air,  in  the  in- 
verse proportion  of  the  refractive  indices.  The  result 
is.  therefore,  decisive  in  favour  of  the  undulatory,  or, 
at  least,  against  the  emission  theory  -°. 

There  is  no  science,  perhaps,  in  which  the  Method 
of  Difference  is  so  extensively  used  as  the  science  of 
('hemistry,  and  that  because  chemistry  is  emphatically  a 
science  of  experiment.  Almost  any  chemical  experiment 
will  serve  as  an  instance  of  the  Method  of  Difference. 
Mix,  for  example,  chloride  of  mercury  with  iodide  of 
potassium,  and  the  result  will  be  a  colourless  liquid  at 
the  top  of  the  vessel  with  a  brilliant  red  precipitate  at 

t)f  the  law«N  of  clastic  fluids,  but  at  most  that  they  are  governed  by 
laws  partially  identical  with  these.'  But,  though  the  experiment  may 
not  be  decisive  as  in  favour  of  the  Undulatory  Theory,  it  is  un- 
doubtedly decisive  as  against  the  Eniissi  m  Theory.  It  may  be 
necessiry  to  add  that  the  term  '  fluids'  would  now  be  repudiated  by 
those  wl  o  hold  the  Undi  latory  Theory. 

'**  Sf^e    Lloyd's   Wave   Theory  of  light,   3rd  ed.  Arts.  41,  42  ; 
(ianot's  PhysicSy  English  translation,  12th  edition,  Art.  506. 


\ 


the  bottom.  There  can  be  no  hesitation  in  ascribing 
this  result  to  the  mixture  of  the  two  liquids ;  and  two 
similar  experiments  will  enable  us  to  determine  that  the 
chlorine  has  been  set  free  from  the  mercury  and  united 
with  the  potassium,  which  itself  has  been  set  free  from 
the  iodine  with  which  it  was  previously  united,  while 
the  iodine  has  united  with  the  mercury,  the  former  pro- 
ducing chloride  of  potassium  (dissolved  in  the  colourless 
liquid),  the  latter  iodide  of  mercury  (the  red  precipitate). 
The  science  of  Heat  (or,  as  Dr.  Whewell  proposes  to 
call  it,  Thermotics)  also  furnishes  excellent  examples  of 
the  Method  of  Difference.  The  following  instances  are 
adapted  from  Professor  Tyndall's  Heat  a  Mode  of 
Motion  '^^  : — 

'  Here  is  a  brass  tube,  four  inches  long,  and  of  three- 
quarters  of  an  inch  interior  diameter.  It  is  stopped  at  the 
bottom  and  screwed  on  to  a  whirling  table,  by  means  of 
which  the  upright  tube  can  be  caused  to  rotate  very  rapidly. 
These  two  pieces  of  oak  are  united  by  a  hinge,  in  which  are 
two  semicircular  grooves,  intended  to  embrace  the  brass  tube. 
Thus  the  pieces  of  wood  form  a  kind  of  tongs,  the  gentle 
squeezing  of  which  produces  friction  when  the  tube  rotates. 
I  partially  fill  the  tube  with  cold  water,  stop  it  with  a  cork 
to  prevent  the  splashing  out  of  the  liquid,  and  now  put  the 
machine  in  motion.  As  the  action  continues,  the  temperature 
of  the  water  rises,  and  now  the  tube  is  too  hot  to  be  held  in 
the  fingers.  Continuing  the  action  a  little  longer,  the  cork 
is  driven  out  with  explosive  violence,  the  steam  which  follows 
it  producing  by  its  precipitation  a  small  cloud  in  the  atmo- 
sphere.' 

21  Third  p:dition,  ch.  i.  §§  14-16. 


156 


INDUCTIVE  METHODS, 


In  this  experiment  it  will  be  noticed  that  only  one  new 
antecedent  is  introduced,  namely  the  motion  of  the  ma- 
chine ;  hence  the  increased  temperature  of  the  water  and 
the  various  effects  which  follow  upon  it  are  due  to  the 
motion  as  a  cause.  The  experiment,  then,  shows  that 
heat  is  generated  by  the  action  of  mechanical  force. 

The  converse  of  this  proposition,  namely  that  heat  is 
consumed  in  mechanical  work,  or,  as  it  is  often  stated, 
transmuted  into  mechanical  energy,  is  proved  by  the  two 
next  experiments. 

*This  strong  vessel  is  filled  at  the  present  moment  with 
compressed  air.  It  has  lain  here  for  some  hours,  so  that  the 
temperature  of  the  air  within  the  vessel  is  now  the  same  as 
that  of  the  air  of  the  room  without  it.  At  the  present  mo- 
ment this  inner  air  is  pressing  against  the  sides  of  the  vessel, 
and  if  this  cock  be  opened  a  portion  of  the  air  will  rush 
violently  out.  The  word  "rush,"  however,  but  vaguely  ex- 
presses the  true  state  of  things  ;  the  air  which  issues  is  driven 
out  by  the  air  behind  it ;  this  latter  accomplishes  the  work  of 
urging  forward  the  stream  of  air.  And  what  will  be  the  con- 
dition of  the  working  air  during  this  process  ?  It  will  be 
chilled.  The  air  executes  work,  and  the  only  agent  it  can 
call  upon  to  perform  the  work  is  the  heat  to  which  the  elastic 
force  with  which  it  presses  against  the  sides  of  the  vessel  is 
entirely  due.  A  portion  of  this  heat  will  be  consumed,  and 
a  lowering  of  temperature  will  be  the  consequence.  Observe 
the  experiment.  I  will  turn  the  cock,  and  allow  the  current 
of  air  from  the  vessel  to  strike  against  the  face  of  the  pile'^'. 

^'^  That  is,  the  ihermo-electric  pile,  a  delicate  instrument  for 
indicating  very  small  changes  of  temperature.  It  is  by  means  of 
this  instrument  that  it  has  recently  been  shown  that  we  receive  heat 
(though,  of  course,  in  infinitesimal  quantities)  from  the  moon's  rays. 


METHOD   OF  DIFFERENCE, 


^Sl 


The  magnetic  needle  instantly  responds  ;  its  red  end  is  driven 
towards  me,  thus  declaring  that  the  pile  has  been  chilled  by 
the  current  of  air.' 

'  Here  moreover  is  a  bottle  of  soda-water,  slightly  warmer 
than  the  pile,  as  you  see  by  the  deflexion  it  produces.  Cut 
the  string  which  holds  it,  the  cork  is  driven  out  by  the  elastic 
force  of  the  carbonic  acid  gas  ;  the  gas  performs  work,  in  so 
doing  it  consumes  heat,  and  now  the  deflexion  produced  by 
the  bottle  is  that  of  cold.' 

The  last  experiment  furnishes  a  good  instance  of  the 
extreme  simplicity  of  the  examples  by  which  scientific 
truths  may  often  be  illustrated. 

The  uncertainty  which,  as  w^e  have  seen,  always  at- 
taches to  conclusions  arrived  at  by  the  Method  of  Agree- 
ment renders  it  desirable  that  they  should,  wherever  it  is 
possible,  be  confirmed  by  an  application  of  the  Method 
of  Difference.  A  beautiful  instance  of  such  a  confirma- 
tion is  adduced  by  Mr.  Mill  in  the  case  of  CrystalHzation. 
The  Method  of  Agreement  has  already  led  us  to  the 
conclusion  that  the  solidification  of  a  substance  from 
a  fluid  state  is  a  very  frequent  antecedent  of  its  crystal- 
lization, and  so,  probably,  one,  at  least,  of  its  causes. 
But  the  Method  of  Difference  completes  the  evidence, 
and  enables  us  to  state  positively  that  it  is  a  cause. 

*  For  in  this  case  we  are  able,  after  detecting  the  antece- 
dent A,  to  produce  it  artificially,  and,  by  findir.g  that  a  follows 
it,  verify  the  result  of  our  induction.  The  importance  of 
thus  reversing  the  proof'was  never  more  strikingly  manifested 
than  when,  by  keeping  a  phial  of  water  charged  with  siliceous 
particles  undisturbed  for  years,  a  chemist  (I  believe  Dr.  Wol- 


158 


INDUCTIVE   METHODS. 


laston)  succeeded  in  obtaining  crystals  of  quartz;  and  in 
the  equally  interesting  experiment  in  which  Sir  James  Hall 
produced  artificial  marble,  by  the  cooling  of  its  materials 
from  fusion  under  immense  pressure  :  two  admirable  ex- 
amples of  the  light  which  may  be  thrown  upon  the  most 
secret  processes  of  nature  by  well-contrived  interrogation 
of  her  '^: 

It  will  be  noticed  that  the  Method  of  Difference  is 
specially  adapted  to  the  discovery  of  the  effects  of  given 
causes,  whereas,  where  it  is  our  object  to  discover  the 
cause  of  a  given  effect,  we  are  usually  compelled  to  have 
recourse  to  the  Method  of  Agreement.  The  Method  of 
Agreement  is,  in  fact,  mainly  a  Method  of  Observation, 
whereas  the  Method  of  Difference  is  mainly  a  Method 
of  Experiment.  We  may  indeed  arrange  the  conditions 
of  an  experiment  so  as  to  satisfy  the  requirements  of 
the  Method  of  Agreement,  and  Nature  may  (as  in  the 
familiar  case  of  lightning)  herself  satisfy  the  requirements 
of  the  Method  of  Difference,  but,  as  a  rule,  it  will  be 
found  that  arguments  based  on  observations  fall  under 
the  former,  and  arguments  based  on  experiments  under 
the  latter  Method.  It  is  hardly  necessary  to  add  that, 
wherever  we  have  our  choice  between  the  two  methods, 
we  should  invariably  select  the  Method  of  Difference. 

^3  Mill's  Logic,  Bk.  III.  ch.  viii.  §  i.  I  have  been  obliged,  in 
accordance  with  what  has  been  said  on  p.  146,  to  state,  with  con- 
siderable modifications,  the  conclusion  in  this  instance  as  arrived 
at  by  the  Method  of  Agreement.  The  account  of  the  application 
to  it  of  the  Method  of  Difference  has  been  stated  in  Mr.  Mill's  own 
words. 


METHOD   OF  DIFFERENCE. 


359 


In  the  employment  of  the  Method  of  Difference,  the 
greatest  care  should  be  taken  to  introduce  only  one  new 
antecedent,  or  at  least  only  one  new  antecedent  which 
can  influence  the  result.      As  the  whole  force  of  the 
argument  based  on  this  Method  depends  on  the  assump- 
tion that  any  change  which  takes  place  in  the  phenome- 
non is  due  to  the  antecedent  then  and  there  introduced, 
it  is  plain  that  we  can  place  no  reliance  on  our  conclusion 
unless  we  feel  perfectly  assured  that  no  other  antecedent 
has  intervened.     If,  for  instance,  it  is  our  object  to  as- 
certain the  temperature  of  the  atmosphere,  we  must  take 
the  greatest  care  that  our  thermometer  is  not  affected 
by  the  heat  radiated  from  or  conducted  by  other  bodies. 
The  most  curious  examples  of  the   disregard   of  this 
caution   may    be   found    in    the    History   of   Medicine. 
Something  perfectly  inert  has  been  administered  to  a 
patient  in  combination  with  some  powerful  drug,  some 
important  alterations  in  his  diet,  or  some  strict  regime ; 
then  the  effects  of  the  drug,  diet,  or  regime  have  been 
unwittingly  ascribed  to  the  inert  substance.      Had  the 
ancients  recognised  that  instead  of  one  cause  acting  on 
falling  bodies,  as  appeared  to  them  to  be  the  case,  there 
were  really  two,  the  action  of  gravity  tending  downwards 
and  the  resistance  of  the  atmosphere  pressing  upwards, 
they  could  never   have   fallen    into  the  gross  error  of 
supposing  that  bodies  fall  in  times  inversely  proportional 
to  their  weights. 


i6o 


INDUCTIVE  METHODS, 


DOUBLE  METHOD  OF  AGREEMENT. 


CANON. 


If  t7V0  or  more  instances  in  which  the  phenomenon  occurs 
have  only  one  other  circumstance  in  common^  while  two  or 
more  instances^  falling  ivithin  the  same  department  of  in- 
vestigation '^^j  frofn  which  the  phenomenon  is  absent  have 
nothing  in  conunon  save  the  absence  of  that  circumstance  ; 
that  circumstance  is  the  effect^  or  the  cause^  or  a  necessary 
part  of  the  cause ^  of  the  phenomenon.  Moreover  {suppositig 
the  requirements  of  the  Method  to  be  rigorously  fulfilled), 
the  circumstance  proved  by  the  Method  to  be  the  cause  is  the 
only  cause  of  the  phenomenon. 

The  uncertainty  attaching  to  the  Method  of  Agreement 
may,  even  where  it  is  impossible  to  have  recourse  to  the 
Method  of  Difference,  be,  to  some  extent,  remedied  by  the 
employment  of  what  is  called  by  Mr.  Mill  the  Joint  Method 
of  Agreement  and  Difference,  or  the  Indirect  Method  of 

■■"  In  recent  editions  I  have  inserted  in  the  statement  of  the  Canon 
the  words  '  falling  within  the  same  department  of  investigation,' 
because,  as  has  been  pointed  out  to  me,  the  student  might  otherwise 
not  see  that,  for  the  purposes  of  comparison,  the  positive  and  negative 
instances  must  be  in  pari  materid.  Thus,  if  the  subject  of  enquiry 
is  language,  the  negative  as  well  as  the  positive  instances  must  be 
sought  in  the  department  of  language  ;  or,  if  the  subject  of  enquiry 
lies  within  the  sphere  of  morals,  or  of  physical  forces,  or  of  living 
organisms,  the  negative  as  well  as  the  positive  instances  must  be 
sought  within  those  respective  departn  ents.  Practically,  however, 
there  is  no  occasion  for  definite  rules  on  this  head,  as  the  common- 
sense  of  the  investigator  is  quite  sufficient  to  keep  him  within  the 
limits  of  the  enquiry. 


DOUBLE  METHOD   OF  AGREEMENT,         l6l 

Difference.  This  Method  consists  in  a  double  employ- 
ment of  the  Method  of  Agreement  and  a  comparison  of 
the  results  thus  obtained,  the  comparison  assimilating  it 
to  the  Method  of  Difference.  We,  first  of  all,  compare 
cases  in  which  the  phenomenon  occurs,  and,  so  far  as  we 
can  ascertain,  find  them  to  agree  in  the  possession  of 
only  one  other  circumstance.  But,  though  we  may  not 
be  justified  in  regarding  this  inference  as  certain,  we  may 
increase  our  assurance  by  proceeding  to  compare  cases 
in  which  the  phenomenon  does  not  occur.  If  these  cases 
agree  in  nothing  but  the  non-possession  of  the  circum- 
stance which  the  other  cases  agreed  in  possessing,  we 
have  a  set  of  negative  instances  agreeing  in  nothing  but 
the  absence  of  the  given  phenomenon  and  the  absence 
of  the  aforesaid  circumstance.  The  set  of  negative 
instances  may  now  be  compared  with  the  set  of  positive 
instances,  and  we  may  argue  thus  :  The  positive  in- 
stances agree  in  nothing  but  the  presence  of  the  given 
phenomenon  and  this  other  circumstance,  and  the  nega- 
tive instances  agree  in  nothing  but  the  absence  of  the 
given  phenomenon  and  this  other  circumstance.  Hence 
we  may  regard  it  as  a  highly  probable  inference  that 
they  are  connected  together  as  cause  and  effect.  I 
say  'highly  probable,'  for,  as  we  are  not  absolutely 
certain  that  the  conditions  of  the  Method  of  Agreement 
have  been  satisfied  in  the  case  of  the  positive  instances, 
so,  from  the  extreme  difficulty  of  proving  a  negative, 
WT  must  be  still  less  certain  that  they  have  been  satisfied 
in  the  case  of  the  negative  instances.     What  (in  addition 

M 


l62 


INDUCTIVE  METHODS, 


to  another  advantage,  to  be  noticed  presently)  is  gained 
by  the  Method  is  a  sort  of  double  assurance,  so  far 
as  the  assurance  goes.  If  the  one  set  of  instances 
agreed  in  nothing  but  the  presence  of  the  two  circum- 
stances, and  //  the  other  set  of  instances  agreed  in 
nothing  but  the  absence  of  the  two  circumstances,  then 
we  should  be  able  to  infer,  by  the  Method  of  Difference, 
that  the  introduction  of  the  given  phenomenon  (which 
we  will  suppose  to  be  the  consequent)  always  follows 
on  the  introduction  of  the  other  circumstance  (which 
we  will  suppose  to  be  the  antecedent),  and,  vice  versa, 
that  the  removal  of  the  given  phenomenon  always  follows 
on  the  removal  of  the  other  circumstance,  or,  in  other 
words,  that  the  given  phenomenon  is  the  effect  and  the 
other  circumstance  the  cause. 

But  this  Method,  supposing  its  conditions  to  be 
rigorously  satisfied,  possesses  one  advantage  peculiar  to 
itself.  The  Single  Method  of  Agreement,  as  we  have 
seen,  is  always  theoretically  open  to  the  objection  arising 
from  Plurality  of  Causes,  but  this  Method,  if  the  set  of 
negative  instances  be  perfect,  is  not  only  free  from  that 
objection,  but  also  sustains  the  conclusion  that  the  in- 
ferred cause  is  the  only  cause  of  the  phenomenon  in 
question  (or,  in  case  we  do  not  know  which  is  ante- 
cedent and  which  is  consequent,  that  a  and  b  are  so 
connected  that  one  of  them  is  the  cause  and  the  only 
cause  of  the  other).  *  In  the  joint  method,'  says  Mr. 
MilP^  *it  is  supposed  not  only  that  the  instances  in 
=»^  Mill's  Logic,  13k.  III.  ch.  x.  §  a. 


DOUBLE  METHOD   OF  AGREEMENT. 


163 


which  a  is  agree  only  in  containing  A,  but  also  that  the 
instances  in  which  a  is  not  agree  only  in  not  containing 
A.  Now,  if  this  be  so,  A  must  be  not  only  the  cause  of 
a,  but  the  only  possible  cause  :  for  if  there  were  another, 
as  for  example  B,  then  in  the  instances  in  which  a  is  not, 
B  must  have  been  absent  as  well  as  A,  and  it  would  not 
be  true  that  these  instances  agree  07ily  in  not  containing 
A,'  It  may  be  asked,  then,  if  the  negative  branch  of  the 
argument  be  so  forcible,  why  should  we  employ  the  posi- 
tive branch  ?  It  is  by  means  of  the  positive  branch  that 
we  are,  as  it  were,  put  on  the  track  of  the  one  other  cir- 
cumstance in  which  the  instances  presenting  the  given 
phenomenon  agree,  and  by  means  of  the  negative  branch 
that  we  prove  the  accuracy  of  our  conclusion.  '  It  is 
generally,'  continues  Mr.  Mill,  '  altogether  impossible  to 
work  the  Method  of  Agreement  by  negative  instances 
without  positive  ones  :  it  is  so  much  more  difficult  to 
exhaust  the  field  of  negation  than  that  of  affirmation.' 

It  is  plain  that  the  conditions  of  the  Joint  Method  can 
only  be  rigorously  fulfilled  where  there  is  an  invariable 
conjunction  between  two  phenomena,  so  that  the  two 
are  (unless  counteracting  circumstances  intervene)  always 
present  together  and  always  absent  together.  For,  if  A 
be  the  only  cause  of  a,  the  effect  a  cannot  be  present 
without  the  cause  A,  nor  can  the  cause  A  be  present 
without  being  attended  by  the  effect  a.  Hence  (bearing  in 
mind,  of  course,  what  has  already^  been  said  on  pp.  48-9^ 
134,  of  the  exclusion  q{  immaterial  circumstances),  invari- 
able conjunction  may  be  regarded  as  a  s'gn  that  the  con- 

M  2 


l64 


INDUCTIVE  METHODS, 


ditions  of  this  Method  are  fulfilled,  and  it  is  from  the 
observation  of  such  an  invariable  conjunction  that  the 
argument  frequently  proceeds.  In  such  cases,  the  number 
of  instances,  both  positive  and  negative,  which  have  been 
observed,  is  supposed  to  be  so  great  and  of  such  variety  as 
to  have  excluded  all  other  common  circumstances  except 
the  presence  or  absence  of  the  two  phenomena  in  question. 

The  Joint  Method  of  Agreement  and  Difference  (or 
the  Indirect  Method  of  Difference,  or,  as  I  should  prefer 
to  call  it,  the  Double  Method  of  Agreement)  is  being 
continually  employed  by  us  in  the  ordinary  affairs  of  life. 
If,  when  I  take  a  particular  kind  of  food,  I  find  that 
I  invariably  suffer  from  some  particular  form  of  illness, 
whereas,  when  I  leave  it  off,  I  cease  to  suffer,  I  entertain 
a  double  assurance  that  the  food  is  the  cause  of  my 
illness.  I  have  observed  that  a  certain  plant  is  invariably 
plentiful  on  a  particular  soil ;  if,  with  a  wide  experience, 
I  fail  to  find  it  growing  on  any  other  soil,  I  feel  con- 
firmed in  my  belief  that  there  is  in  this  particular  soil 
some  chemical  constituent,  or  some  peculiar  combination 
of  chemical  constituents,  which  is  highly  favourable,  if 
not  essential,  to  the  growth  of  the  {jlant. 

Dr.  Wells'  Essay  on  the  Theory  of  Dew  presents  an 
extremely  instructive  instance  of  the  application  of  the 
Double  Method  of  Agreement : — 

*  It  appears'  (I  am  here  quoting  from  Mr.  Mill  ^^)  'that  the 
instances  in  which  much  dew  is  deposited,  which  are  very 
various,  agree  in  this,  and,  so  far  as  we  are  able  to  observe, 
20  Miii'g  iggi^^  Bk.  III.  ch.  ix.  §  3. 


DOUBLE  METHOD   OF  AGREEMENT,         1 65 

in  this  only,  that  they  either  radiate  heat  rapidly  or  conduct 
it  slowly  :  qualities  between  which  there  is  no  other  circum- 
stance of  agreement  than  that,  by  virtue  of  either,  the  body 
tends  to  lose  heat  from  the  surface  ifiore  rapidly  than  it  can 
be  restored  from  within.  The  instances,  on  the  contrary,  in 
which  no  dew,  or  but  a  small  quantity  of  it,  is  formed,  and 
which  are  also  extremely  various,  agree  (as  far  as  we  can 
observe)  in  nothing  except  in  not  having  this  same  property. 
We  seem,  therefore,  to  have  detected  the  characteristic 
difference  between  the  substances  on  which  dew  is  produced, 
and  those  on  which  it  is  not  produced.  And  thus  have  been 
realized  the  requisitions  of  what  we  have  termed  the  Indirect 
Method  of  Difference,  or  the  Joint  Method  of  Agreement 
and  Difference.' 

Several  beautiful  illustrations  of  the  Joint  Method  of 
Agreement  and  Difference  may  be  found  in  the  recent 
discoveries  made  by  means  of  Spectrum  Analysis.  I 
shall  select  one  which  is  peculiarly  interesting  on  account 
of  its  employment  in  the  attempt  to  determine  the  consti- 
tution of  the  sun  and  some  of  the  other  heavenly  bodies. 

A  very  thin  sheet  of  light  proceeding  from  incandescent 
hydrogen  is  passed  through  a  prism,  and  it  is  invariably 
found  (with  the  exception  of  the  third  case  mentioned  in 
note  27)  that  in  the  spectrum  thus  obtained  there  are,  in 
proportion  to  the  intensity  of  the  light,  one,  two,  or 
more  bright  lines  occupying  precisely  the  same  rela- 
tive position.  Moreover,  very  thin  sheets  of  white 
light  proceeding  from  various  incandescent  substances 
are  passed  through  incandescent  hydrogen,  and  the 
emergent  light  is  then  separated  into  its  constituent 
elements  by  a  prism.     In  the  spectra  thus  obtained  it  is 


1 66 


INDUCTIVE  METHODS, 


found  that  there  are  invariably  (with  the  above-named 
exception)  dark  (or,  under  certain  circumstances,  bright") 
hnes  occupying  exactly  the  same  positions  in  the  spectrum 
as  the  lines  above  mentioned.  Hence  it  is  inferred,  by 
the  Method  of  Agreement,  that  a  sheet  of  light,  whether 
it  proceed  directly  from  incandescent  hydrogen  itself,  or 
be  transmitted  through  it  from  some  other  incandescent 
substance,  will  (allowing  for  the  above  exception)  invari- 
ably produce  these  lines.  But,  if  we  try  the  same 
experiments  with  any  other  element  than  incandescent 
hydrogen,  although  we  may  obtain  bright  or  dark  lines, 
we  never  find  these  lines  occupying  the  same  positions 
in  the  spectrum  as  the  lines  in  question. 

Here,  then,  we  have  the  negative  instances  of  the 
Double  Method  ;  and  it  is  inferred  (subject,  of  course,  to 
the  assumption  that  our  knowledge  of  the  negative  in- 
stances is  sufficiently  complete)  that  the  presence  in  the 
spectrum  of  these  lines  is  invariably  due  either  to  a  sheet 
of  light  proceeding  directly  from  incandescent  hydrogen, 
or  to  a  sheet  transmitted  through  it  from  some  other 
incandescent  substance  ;  that  is  to  say,  that  one  or  other 
of  these  is  the  cause,  and  the  ojily  cause  of  the  presence 

-'  The  darkness  of  the  lines  is  due  to  the  property  possessed  by 
incandescent  media  of  absorbing  sheets  of  light  of  the  same  refran- 
gibility  as  those  emitted  by  them.  When  the  absorption  exerted 
upon  the  transmitted  light  is  more  than  compensated  by  the  luminosity 
of  the  hydrogen  light,  these  lines,  instead  of  being  dark,  appear 
bright,  as  is  also  the  case  when  the  sheet  of  light  proceeds  directly 
from  incandescent  hvdrogen  itself.  There  is  still  a  third  case.  When 
the  hydrogen  emits  as  much  light  as  it  absorbs,  there  will  be  no  line, 
dark  or  bright. 


DOUBLE  METHOD   OF  AGREEMENT,         167 

in  the  spectrum  of  these  particular  lines.  When  these 
lines  are  bright,  it  is  doubtful  whether  the  rays  proceed 
directly  from  incandescent  hydrogen  or  have  been 
transmitted  through  it,  but,  when  they  are  dark,  the 
sheets  must  have  been  transmitted.  Wherever,  there- 
fore, dark  lines  occupying  these  positions  occur  in 
the  spectrum  we  may  infer  (deductively)  the  passage 
of  the  sheet  of  light  through  a  medium  composed  wholly 
or  partially  of  incandescent  hydrogen.  But  we  detect 
such  lines  in  the  spectrum  of  the  sun  and  several  of 
the  stars,  and  hence  (unless  we  suppose  it  possible  or 
not  improbable  that  there  is  in  the  sun  or  other  stars 
some  element  agreeing  in  this  respect  with  hydrogen, 
but  differing  in  others)  we  may  conclude  that  the  sun 
and  these  other  stars  are  surrounded  with  an  atmo- 
sphere of  incandescent  hydrogen  '^ 

The  following  examples  are  selected  from  a  subject  of 
a  widely  different  character,  the  History  of  Language. 
M.  Auguste  Brachet,  in  his  Historical  Grammar  of  the 

^  It  must  be  understood  that,  in  this  example,  I  have  not  stated 
the  historical  steps  by  which  the  discovery  was  arrived  at,  but 
simply  attempted  to  give  a  logical  analysis  of  the  arguments  by 
which  it  would  now  be  established.  It  was  the  exact  coincidence  of 
the  bright  lines  in  the  hydrogen  spectrum  with  the  dark  lines  in  the 
solar  spectrum,  which  first  led  to  the  belief  that  hydrogen  enters  into 
the  constitution  of  the  solar  atmosphere.  It  is  now,  however,  ren- 
dered possible,  through  an  ingenious  contrivance,  to  separate,  as  it 
were,  the  solar  atmosphere  from  the  glowing  body  within  it,  and  thus 
to  obtain  these  lines  bright  instead  of  dark.  The  student  will  find  a 
brief  account  of  these  discoveries  in  Professor  Stokes'  Address  to  the 
British  Association  in  1869. 


i68 


INDUCTIVE  METHODS. 


French  Tongue'^^,  lays  down  the  position  that  there  are 
three  sure  tests  by  which  we  can  discriminate  between 
popular  words  derived  from  the  Peasant  Latin  (lingua 
Latina  rustica)  by  a  regular  process,  and  Latin  words  of 
learned  origin  imported  into  Modern  French  by  scholars. 
These  tests  are  (i)  the  continuance  of  the  tonic  accent ; 
(2)  the  suppression  of  the  short  vowel ;  (3)  the  loss  of  the 
middle  or  medial  consonant.  It  will  be  seen  that  it  is  by 
the  employment  of  the  Double  Method  of  Agreement 
that  M.  Brachet  arrives  at  these  conclusions. 


'  Look  at  such  words  ;i.  e.  words  of  popular  origin)  carefully,  and 
you  will  see  that  the  syllable  accented  in  Latin  continues  to  be  so  in 
French  ;  or,  in  other  words,  that  the  accent  remains  where  it  was  in 
Latin.  This  continuance  of  the  accent  is  a  general  and  absolute  law  : 
all  words  belonging  to  popular  and  real  French  respect  the  Latin 
accent  ;  all  such  words  as  portiqtie  from  p6rticua,  or  viatique  from 
vidticum,  which  break  this  law,  will  be  found  to  be  of  learned 
origin,  introduced  into  the  language  at  a  later  time  by  men  who 
were  ignorant  of  the  laws  which  nature  had  imposed  on  the  transfor- 
mation from  Latin  to  French.  We  may  lay  it  down  as  an  infallible 
law,  that  The  latin  accent  continues  in  French  in  all  words  of 
popular  origin  ;   all  words   whicJi  violate  this   la'iu  are  of  learned 


origin  :  thus — 

LATIN. 

POPULAR    WORDS. 

LEARNED    WOF 

Aliimine 

aliin 

alumine 

Angelas 

dnge 

angeliis 

Bldsphemum 

bldme 

blaspheme 

Cdncer 

chancre 

cancer 

Computura 

c6mpte 

compiit 

D^bitum 

dette 

debit 

D^cima 

dime 

decime^  &c. 

'^  Dr.  Kitchin's  Translation,  p.  32,  7th  ed.  pp.  44-48. 


DOUBLE  METHOD   OF  AGREEMENT 


169 


*  We  have  seen  that  the  tonic  accent  is  a  sure  touchstone  by  which 
to  distinguish  popular  from  learned  words.  There  is  another  means, 
as  certain,  by  which  to  recognise  the  age  and  origin  of  words — the 
loss  of  the  short  vowel.  Every  Latin  wofd,  as  we  have  said,  is 
made  up  of  one  accented  vowel,  and  others  not  accented — one  tonic 
and  others  atonic.  The  tonic  always  remains  ;  but  of  the  atonies  the 
short  vowel,  which  immediately  precedes  the  tonic  vowel,  always  dis- 
appears in  French  :  as  in — 

Bon(i)tdtera  bonte 

S  an  (i  titem  sante 

Pos^X)tura  posture 

Clar(i)tdteni  clarte 

Sep(trindna  semaine  (O.  Fr.  sepmaine) 

Com  ( i)  tdtu  s  comti 

Pop(ii)16,tus  peupU^  &c. 

•  Words  such  as  circuler,  circuldre,  which  break  this  law  and 
keep  the  short  vowel,  are  always  of  learned  origin  ;  all  words  of 
popular  origin  lose  it,  as  cercler.  This  will  be  seen  from  the  follow- 
ing examples  : — 

LATIN.  POPULAR   WORDS.  LEARNED   WORDS. 

Ang;u  latus  angle  angtile 

Blasph(e  mdre        bldmer  (C).Yr.  blasmcr)  blasphemer 

Cap(i;t^le  cheptel  capital 

Car(i)tdtem  cherts  charite 


Circfu^ldre 


cercler 


circuler ^  &c. 


*  The  third  characteristic,  serving  to  distinguish  popular  from 
learned  words,  is  the  loss  of  the  medial  consonant,  i.e.  of  the  con- 
sonant which  stands  between  two  vowels,  like  the  t  in  maturus. 
We  will  at  once  give  the  law  of  this  change  : — All  French  words 
which  drop  the  medial  consonant  are  popular  in  origin,  while  words 
of  learned  origin  retain  it.  Thus  the  Latin  vocalis  becomes,  in 
popular  French,  voyelle,  in  learned  French,  vocale.  There  are  innu- 
merable examples  of  this  :  as — 

LATIN.        POPULAR  WORDS.    LEARNED  WORDS. 

Au(g)iistus  aoiit  auguste 

Advo(c^6tus  avoue  avocat 


170 


INDUCTIVE  METHODS. 


LATIN. 

Anti(ph)6na 
Cre(d)6ntia 
Communi  (c)  Are 


POPULAR    WORDS. 

antienne 

crcance 

commiinicr 


LEARNED   WORDS. 

antiphone 
credence 
conimiotiquer^  &c.* 


The  requisitions  of  the  Double  Method  of  Agreement 
may  be  far  from  being  rigorously  fulfilled,  and  still 
two  phenomena  may  be  so  frequently  present  together 
and  so  frequently  absent  together,  that  we  may  be  justi- 
fied in  suspecting  some  causal  connexion  between  them. 
Unless  they  were  invariably  absent  together,  as  well  as 
invariably  present,  and  unless  they  were  the  otily  cir- 
cumstances which  were  invariably  present  and  absent 
together,  we  should  not  be  justified  in  regarding  one  as 
the  cause,  and  the  only  cause,  of  the  other  ;  but  the  mere 
detection  of  the  fact  that  they  are  frequently  present  and 
absent  together  may  justify  us  in  believing  that  there 
is  between  them  some  causal  connexion.  The  precise 
character  of  this  causal  connexion  may  hereafter  be 
determined  by  one  of  the  other  inductive  methods,  or 
by  bringing  the  case  under  a  previous  deduction.  The 
following  instances  will  serve  as  illustrations  of  what  has 
been  here  said. 

Sir  John  Herschel  conceives  that  he  has  detected  a 
connexion  between  a  full  moon  and  a  calm  night :  *  The 
only  effect  distinctly  connected  with  its  [the  moon's] 
position  with  regard  to  the  sun,  which  can  be  reckoned 
upon  with  any  degree  of  certainty,  is  its  tendency  to  clear 
the  sky  of  cloud,  and  to  produce  not  only  a  serene  but  a 
calm  night,  when  so  near  the  full  as  to  appear  round  to 


DOUBLE  METHOD  OF  AGREEMENT, 


171 


the  eye— a  tendency  of  which  we  have  assured  ourselves 
by  long-continued  and  registered  observation.'  The  pre- 
cise nature  of  the  causal  connexioi;  can  here  be  deter- 
mined :  '  The  effect  in  question,  so  far  as  the  clearance 
of  the  sky  is  concerned,  is  traceable  to  a  distinct  physical 
cause,  the  warmth  radiated  from  its  [the  full  moon's] 
highly-heated  surface ;  though  why  the  effect  should 
not  continue   for  several   nights  after  the  full,  remains 

problematic^^' 

In  this  example,  there  is  not,  of  course,  an  invariable 
connexion  between  the  clear  night  and  the  full  moon  ; 
for,  in  the  determination  of  the  weather,  there  are  so 
many  and  so  various  causes  at  work  that  they  must 
necessarily  modify  or  counteract  each  other.  The  moon 
might  exercise  considerable  influence,  might,  as  Sir  John 
Herschel  says,  have  a  tendency  to  produce  a  calm  night 
and  still  be  overpowered  by  other  influences.  It  is  suffi- 
cient, in  order  to  lead  us  to  suspect  some  causal  con- 
nexion between  the  two  phenomena,  that  we  should  find 
a  calm  night  proportionably  oftener,  and  oftener  in  a 
considerable  proportion,  when  there  is  a  full  moon  than 
when  there  is  not.  Thus,  suppose  that,  after  a  long 
series  of  observations  of  nights  when  there  is  a  full 
moon,  we  find  the  proportion  of  calm  nights  to  nights 
which  cannot  be  called  calm  to  be  as  5  to  2  (I  am,  of 
course,  taking  an  imaginary  case),  and  the  proportion  on 
ordinary  nights  to  be  as  3  to  2,  there  can  be  little  doubt 

»  Herschel's  Familiar  Lectures  on  Scientific  Subjects,   pp.  146, 
147. 


1J2 


INDUCTIVE  METHODS, 


that  the  full  moon  is,  in  some  way  or  other,  connected 
with  the  larger  proportion  of  calm  nights. 

The  employment  of  the  Double  Method  of  Agreement 
may  lead  to  the  detection  of  facts  of  causation  in  many 
instances  of  a  similar  kind.     Thus,  suppose  that,  in  a 
particular  part  of  the  country,  a  particular  wind  is  found 
to   be   proportionably  oftener  attended  with  rain   than 
other  winds,  we  begin  to   suspect   that   there  is  some 
causal  connexion  between  rain  and  this  wind,  so  that, 
when  the  wind  blows,  we  may  expect  rain,  at  least  with 
more  confidence  than  when  other  winds  blow  ;  and,  if  the 
proportion  in  which  rain  accompanies  this  wind  be  much 
greater  than  that  in  which  it  accompanies  other  winds, 
our  expectation  is  proportionably  strengthened,  and  we 
have  no  hesitation  in  speaking  of  the  quarter  from  which 
the  wind  blows  as  *  the  rainy  quarter.'     In  this  case,  the 
cause  is,  of  course,  to  be  sought  in  the  character  of  the 
tract   over  which    the  wind   blows.     Similarly,   if,  after 
sufficiently  long  observation,  we  find  the  death-rate  in 
some  particular  place  decidedly  larger  than  in  the  sur- 
rounding neighbourhood,  we  have  no  hesitation  in  ascrib- 
ing the  fact  to  some  peculiarity  either  in  the  place  or  the 
population,  and  we  at  once  begin  to  consider  whether 
there  is  anything  exceptional  in  the  soil,  the  climate,  the 
habits  or  occupations  of  the  people,  and  the  like,  which, 
either  alone  or  in  conjunction  with  other  circumstances, 
would  account  for  the  phenomenon. 

In  all  cases  of  this  kind,  we  are,  as  it  were,  set  on  the 
track  of  a  cause  by  discovering  that  some  phenomenon  is 


METHOD   OF  RESIDUES, 


173 


present  in  a  proportionably  greater  number  of  instances 
when  some  other  phenomenon  is  present  than  when  it  is 
absent.  The  cause  itself  may  herea5:er  be  detected  either 
by  one  of  the  other  inductive  methods,  or  by  bringing  the 
case  under  a  previous  deduction.  Thus,  we  know  that 
the  surface  of  that  part  of  the  moon  which  we  call  '  full ' 
is  highly  heated,  and  that  it  is  the  tendency  of  warmth 
radiated  from  a  highly-heated  surface  to  clear  the  atmo- 
sphere. Hence  the  series  of  observed  phenomena  is, 
in  this  case,  accounted  for  by  being  brought  deductively 
under  previous  inductions. 


METHOD  OF  RESIDUES. 

CANON. 

Subtract  from  any  phenomenon  such  part  as  is  known 
to  be  the  effect  of  certain  antecedejits,  and  the  residue  of  the 
phenomenon  is  the  effect  of  the  remaifiing  antecedents. 

If  the  antecedents  are  A,  B,  C,  D,  and  the  complex 
phenomenon  can  be  resolved  into  the  consequents  o,  ^, 
-y,  8,  f,  of  which  7,  8,  f  are  ascertained  by  previous  induc- 
tions or  deductions  to  be  due  to  C,  D,  then  the  remain- 
ing consequents  a,  3  must  be  referred  to  the  remaining 
antecedents  A,  B.  Given  that  the  total  result  is  due  to  a 
certain  number  of  antecedents,  and  that  part  of  the  result 
is  due  to  a  portion  of  those  antecedents ;  the  residue 
of  the  result  must  necessarily  be  due  to  the  remaining 
antecedents.  This  rule  appears  so  obvious  as  to  be 
hardly  worth   stating;  it  has,  however,  as  will  be  seen 


^74 


INDUCTIVE  METHODS, 


from  the  examples  given  below,  been  mainly  instrumental 
in  leading  to  many  of  the  most  important  discoveries  of 
modern  times.  '  It  is  by  this  process,  in  fact,'  says  Sir 
John  Herschel^  'that  science,  in  its  present  advanced 
state,  is  chiefly  promoted.  Most  of  the  phenomena  which 
nature  presents  are  very  complicated;  and  when  the 
effects  of  all  known  causes  are  estimated  with  exactness, 
and  subducted,  the  residual  facts  are  constantly  appearing 
in  the  form  of  phenomena  altogether  new,  and  leading 
to  the  most  important  conclusions.' 

There  is  one  difficulty  connected  with  this  Method. 
Subtraction  being  a  deductive  process,  why  is  the  Method 
of  Residues  included  among  the  inductive  methods  ?   The 
Method,  it  must  be  confessed,  is  rather  of  a  deductive 
than  an  inductive  character,  but  as,  in  assigning  the  re- 
sidual consequent  to  the  residual  antecedent,  we  assume 
the  Law  of  Universal  Causation,  and  as,  moreover,  the 
method  is  generally  applied  to  the  result  of  previous  in- 
ductions and  generally  suggests  subsequent  inductions,  it 
may  vindicate  its  claim  to  discussion  in  this  place.     It  is 
by  induction  that  we  usually  ascertain  that  y,  8,  e  are  due 
to  C,  D ;  by  the  Method  of  Residues  we  determine  that 
the  remaining  consequents  a,  ^  must  be  due  to  the  re- 
maining antecedents  A,  B ;  we  then  generally  proceed  to 
decide  by  one  of  the  other  inductive  methods  which  of 
the  remaining  consequents  is  due   to  which  of  the  re- 
maining antecedents. 

The  following  are  instances  of  the  employment  of  the 

"  Discourse  on  the  Study  of  Natural  rhilosophy^  §  158. 


METHOD  OF  RESIDUES, 


^75 


Method  of  Residues,  and  it  will  be  noticed  that  the 
science  of  astronomy  is  peculiarly  rich  in  such  ex- 
amples ^^ : —  » 

*The  planet  Jupiter  is  attended  by  four  satellites  which 
revolve  round  it  in  orbits  very  nearly  circular,  and  whose 
dimensions,  forms,  and  situations  with  respect  to  those  of  the 
planet  itself  are  now  perfectly  well  known.  The  periodical 
times  of  their  respective  revolutions  are  also  ascertained  with 
extreme  precision,  and  all  the  particulars  of  their  motions 
have  been  investigated  with  extraordinary  care  and  persever- 
ance. The  three  interior  of  them  are  so  near  the  planet,  and 
the  planes  of  their  orbits  so  little  inclined  to  that  in  which  it 
revolves  round  the  sun,  that  they  pass  through  its  shadow, 
and  therefore  undergo  eclipse,  at  every  revolution.  These 
eclipses  have  been  assiduously  observed  ever  since  the  dis- 
covery of  the  satellites,  and  their  times  of  occurrence 
registered.  As  they  afford  a  means  of  determining  the 
longitudes  of  places,  the  prediction  beforehand  of  the  exact 
times  of  their  occurrence  becomes  an  object  of  great  import- 
ance :  and  it  is  evident  enough  that,  all  the  particulars  of 
their  motions  being  known  (as  well  as  of  that  of  the  planet 
itself,  and  therefore  of  the  size  and  situation  of  its  shadow), 
there  would  be  no  difficulty  in  making  such  prediction 
(starting  from  the  time  of  some  one  observed  eclipse  of  each 
as  an  epoch)  ;  provided  always  each  eclipse  were  seen  at  the 
identical  moment  when  it  actually  happened.  Moreover,  on 
that  supposition,  the  times  recorded  of  all  the  subsequent 

"  In  the  first  and  second  editions  the  acceleration  (or  diminution 
of  the  periodic  times)  of  Encke's  comet  (see  Herschel's  Discourse 
on  the  Study  of  Natural  Philosophy,  §  159)  was  given  as  an  example 
of  residual  phenomena.  The  cause  of  this  phenomenon  is,  however, 
so  doubtful,  that  1  have  thought  it  best  to  omit  the  instance  in  the 
later  editions. 


176 


INDUCTIVE  METHODS, 


eclipses  ought  to  agree  with  the  times  so  predicted.     This, 
however,  proved  not  to  be  the  case.     The  observed  times 
were  sometimes  earlier,  sometimes  later  than  the  predicted  ; 
not,  however,  capriciously,  but  according  to  a  regular  law  of 
increase  and  decrease  in  the   amount  of  discordance,  the 
difference    either    way    increasing    to    a    maximum,— then 
diminishing,  vanishing,  and  passing  over  to  a  maximum  the 
other  way,  and  the  total  amount  of  fluctuation  to  and  fro 
being  about  16"^  27s.     Soon  after  this  discrepancy  between 
the  predicted  and  observed  times  of  eclipse  was  noticed,  it 
was  suggested  that  such  a  disagreement  would  necessarily 
arise  if  the   transmission   of  light  were  not  instantaneous. 
This  suggestion  was  converted  into  a  certainty  by  Roemer,  a 
Danish  astronomer,  who  ascertained  that  they  always  hap- 
pened earlier  than  their  calculated  time  when  the  earth  in 
the  course  of  its  annual  revolution  approached  nearest  to 
Jupiter,  and  later  when  receding  farthest :  so  that  in  effect 
the  extreme  difference  of  the  errors  or  total  extent  of  fluctua- 
tion- the  16™  27'  in  question  — is  no  other  than  the  time 
taken  by  light  to  travel  over  the  diameter  of  the  earth's  orbit, 
that  being  the  extreme  difference  of  the  distances  of  the  two 
planets  at  different  points  of  their  respective  revolutions.    At 
present,  in  our  almanacs  a  due  allowance  of  time  for  the 
transmission  of  light  at  this  rate,  assuming  a  uniform  velocity, 
is  made  in  the  calculation  of  these  eclipses ;   and  the  dis- 
crepancy in   question  between  the  observed  and   predicted 
times  has  ceased  to  exist  ■'^' 

The  circumstances  which  led  to  the  discovery  of  the 
planet  Neptune  furnish,  perhaps,  the  most  striking  in- 
stance of  the  employment  of  the  Method  of  Residues. 
From  the  year  1804  it  had  been  noticed  that  the  orbit 
of  the  planet  Uranus  was  subject  to  an  amount  of  per- 

*•*'  Hcrschers  lamiliar  Lectures  on  Scientific  Subject Sy,  p.  226,  &c. 


METHOD  OF  RESIDUES. 


177 


turbation  which  could  not  be  accounted  for  from  the 
influence  of  the  known  planets. 

*  Of  the  various  hypotheses  formed  to  account  for  it  (the 
perturbation),  during  the  progress  of  its  development,  none 
seemed  to  have  any  degree  of  rational  probability  but  that  of 
the  existence  of  an  exterior,  and  hitherto  undiscovered, 
planet,  disturbing,  according  to  the  received  laws  of  planetary 
disturbance,  the  motion  of  Uranus  by  its  attraction,  or  rather 
superposing  its  disturbance  on  those  produced  by  Jupiter  and 
Saturn,  the  only  two  of  the  old  planets  which  exercise  any 
sensible  disturbing  action  on  that  planet.  Accordingly,  this 
was  the  explanation  which  naturally,  and  almost  of  necessity, 
suggested  itself  to  those  conversant  with  the  planetary  per- 
turbations who  considered  the  subject  with  any  degree  of 
attention.  The  idea,  however,  of  setting  out  from  the 
observed  anomalous  deviations,  and  employing  them  as  data 
to  ascertain  the  distance  and  situation  of  the  unknown  body, 
or,  in  other  words,  to  resolve  the  inverse  problem  of  pertur- 
bations, ''given  the  disturbances  to  find  the  orbit  and  place  in 
that  orbit  of  the  disturbing  planet ;'  appears  to  have  occurred 
only  to  two  mathematicians,  Mr.  Adams  in  England  and 
M.  Leverrier  in  France,  with  sufificient  distinctness  and  hope- 
fulness of  success  to  induce  them  to  attempt  its  solution. 
Both  succeeded,  and  their  solutions,  arrived  at  with  perfect 
independence,  and  by  each  in  entire  ignorance  of  the  other's 
attempt,  were  found  to  agree  in  a  surprising  manner  when 
the  nature  and  difficulty  of  the  problem  is  considered  ;  the 
calculations  of  M.  Leverrier  assigning  for  the  heliocentric 
longitude  of  the  disturbing  planet  for  the  23rd  Sept.  1846, 
326°  o',  and  those  of  Mr.  Adams  (brought  to  the  same  date) 
329"  19',  differing  only  3°  19';  the  plane  of  its  orbit  deviating 
very  slightly,  if  at  all,  from  that  of  the  ecliptic. 

'  On  the  day  above  mentioned— a  day  for  ever  memorable 
in  the  annals  of  astronomy— Dr.  Galle,  one  of  the  astronomers 

N 


178 


INDUCTIVE  METHODS, 


of  the  Royal  Observatory  at  Berlin,  received  a  letter  from 
M.  Leverrier,  announcing  to  him  the  result  he  had  arrived 
at,  and  requesting  him  to  look  for  the  disturbing  planet  in 
or  near  the  place  assigned  by  his  calculation.  He  did  so,  and 
on  that  very  night  actually  found  it.  A  star  of  the  eighth 
magnitude  was  seen  by  him  and  by  M.  Encke  in  a  situation 
where  no  star  was  marked  as  existing  in  Dr.  Bremiker's 
chart,  then  recently  published  by  the  Berlin  Academy.  The 
next  night  it  was  found  to  have  moved  from  its  place,  and 
vv^as  therefore  assuredly  a  planet.  Subsequent  observations 
and  calculations  have  fully  demonstrated  this  planet,  to  which 
the  name  of  Neptune  has  been  assigned,  to  be  really  that 
body  to  whose  disturbing  attraction,  according  to  the  New- 
tonian law  of  gravity,  the  observed  anomalies  in  the  motion 
of  Uranus  were  owing  '*.' 

Besides  furnishing  an  instance  of  the  method  of  Resi- 
dues, the  above  example  is  also  a  happy  illustration  of 
the  combination  of  deduction  with  observation  which  has 
been  so  eminently  fertile  in  astronomical  research. 

*  Almost  all  the  greatest  discoveries  in  astronomy  have 
resulted  from  the  consideration  of  what  we  have  elsewhere 
termed  residual  phenomena,  of  a  quantitative  or  numerical 
kind,  that  is  to  say,  of  such  portions  of  the  numerical  or 
quantitative  results  of  observation  as  remain  outstanding  and 
unaccounted  for  after  subducting  and  allowing  for  all  that 
would  result  from  the  strict  application  of  known  principles. 
It  was  thus  that  the  grand  discovery  of  the  precession  of  the 
equinoxes  resulted,  as  a  residual  phenomenon,  from  the  im- 
perfect explanation  of  the  return  of  the  seasons  by  the  return 
of  the  sun  to  the  same  apparent  place  among  the  fixed  stars. 
Thus,  also,  aberration  and  nutation  resulted  as  residual 
phenomena  from  that  portion  of  the  changes  of  the  apparent 

'*  Herschel's  Outlines  of  Astronomy,  Fourth  Edition,  §§  767,  768. 


METHOD   OF  RESIDUES, 


179 


places  of  the  fixed  stars  which  are  left  unaccounted  for  by 
precession.  And  thus  again  the  apparent  proper  motions  of 
the  stars  are  the  observed  residues  of  their  apparent  move- 
ments outstanding  and  unaccounted*for  by  strict  calculation 
of  the  effects  of  precession,  nutation,  and  aberration.  The 
nearest  approach  which  human  theories  can  make  to  per- 
fection is  to  diminish  this  residue,  this  caput  tnortuum  of 
observation,  as  it  may  be  considered,  as  much  as  practicable, 
and,  if  possible,  to  reduce  it  to  nothing,  either  by  showing 
that  something  has  been  neglected  in  our  estimation  of 
known  causes,  or  by  reasoning  upon  it  as  a  new  fact,  and  on 
the  principle  of  the  inductive  philosophy  ascending  from  the 
effect  to  its  cause  or  causes  ^*.' 

*Many  of  the  new  elements  of  chemistry  have  been 
detected  in  the  investigation  of  residual  phenomena.  Thus, 
Arfwedson  discovered  lithia  by  perceiving  an  excess  of  weight 
in  the  sulphate  produced  from  a  small  portion  of  what  he 
considered  as  magnesia  present  in  a  mineral  he  had  analysed. 
It  is  on  this  principle,  too,  that  the  stnall  concentrated  residues 
of  great  operations  in  the  arts  are  almost  sure  to  be  the 
lurking  places  of  new  chemical  ingredients  :  witness  iodine, 
brome,  selenium,  and  the  new  metals  accompanying  platina 
in  the  experiments  of  Wollaston  and  Tennant.  It  was  a 
happy  thought  of  Glauber  to  examine  what  everybody  else 
threw  away^V 

*The  unforeseen  effects  of  changes  in  legislation,  or  of 
improvements  in  the  useful  arts,  may  often  be  discerned  by 
the  Method  of  Residues.  In  comparing  statistical  accounts, 
for  example,  or  other  registers  of  facts,  for  a  series  of  years, 
we  perceive  at  a  certain  period  an  altered  state  of  circum- 
stances, which  is  unexplained  by  the  ordinary  course  of 
events,  but  which  must  have  some  cause.    For  this  residuary 

^  Herschel's  Outlines  of  Astronomy,  §  856. 

^  Hci^hd'^  Discourse  on  the  Study  of  Natural  Philosophy ^  §  161. 

N  2 


i8o 


INDUCTIVE  METHODS, 


phenomenon,  we  seek  an  explanation  until  it  is  furnished  by 
the  incidental  operation  of  some  collateral  cause.    For  ex- 
ample, on  comparing  the  accounts  of  live  cattle  and  sheep 
annually  sold  in  Smithfield  market  for  some  years  past,  it 
appears  that  there  is  a  large  increase  in  cattle,  while  the  sheep 
are  neariy  stationary.     The  consumption  of  meat  in  London 
may  be  presumed  to  have  increased,  at  least  in  proportion  to 
the  increase  of  its  population ;    and  there  is  no  reason  for 
supposing  that  the  consumption  of  beef  has  increased  faster 
than  that  of  mutton.     There  is,  therefore,  a  residuary  pheno- 
menon—viz. the  stationary  numbers   of  the   sheep  sold  in 
Smithfield— for  which  we  have  to  find  a  cause.    This  cause 
is  the  increased  transport  of  dead  meat  to  the  metropolis, 
owing  to  steam  navigation  and  railways,  and  the  greater  con- 
venience of  sending  mutton  than  beef  in  a  slaughtered  state. 
*  Again  :  on  comparing  the  consumption  of  wine  with  that 
of  spirits  and  beer  in  England  during  the  last  sixty  years  ^^ 
we  find  that  the  former  has  remained  stationary,  while  the 
latter  has  undergone  a  great  increase.     The  general  causes, 
such   as   increase  of  population    and   wealth,   which  have 
increased  the  consumption  of  spirits  and  beer,  have  not 
increased   the  consumption  of  wine.      For  this   residuary 
phenomenon,  a  special  cause  must  be  sought ;  and  it  may  be 
found  principally  in  the  alteration  of  habits  among  the  upper 
classes  with  respect  to  drinking  *V 

3'  This  passage  was  written  in  1852.  Since  that  time,  owing  to 
the  rcduclion  of  the  duties,  the  greater  familiarity  of  Englishmen 
with  foreign  countries  and  habits,  and,  perhaps,  the  taste  for  a  more 
refined  style  of  living,  the  consumption  of  wine  has  enormously  in- 
creased (First  Edition,  1870).  On  the  other  hand,  owing  to  the 
spread  of  Temperance  Societies,  and  of  more  temperate  habits  in  all 
classes,  the  consumption  of  all  alcoholic  drinks  has  now,  for  some 
years,  been  steadily  diminishing,  in  proportion  to  the  population. 

^  Sir  George  Cornewall  Lewis  on  the  Methods  of  Observation  and 
Reasoning  in  Politics,  vol.  i.  p.  356. 


METHOD   OF  RESIDUES. 


181 


I  shall  conclude  my  instances  with  what  Sir  John 
Herschel  truly  calls  *a  very  elegant  example,'  the  dif- 
ference between  the  observed  and*  calculated  velocities 
of  sound.  I  quote  from  Professor  Tyndall's  Lectures 
on  Sound: — 

*  I  now  come  to  one  of  the  most  delicate  points  in  the 
whole  theory  of  sound.  The  velocity  through  air  has  been 
determined  by  direct  experiment ;  but  knowing  the  elasticity 
and  density  of  the  air,  it  is  possible  without  any  experiment 
at  all  to  calculate  the  velocity  with  which  a  sound-wave  is 
transmitted  through  it.  Sir  Isaac  Newton  made  this  calcu- 
lation, and  found  the  velocity  at  the  freezing  temperature  to 
be  916  feet  a  second.  This  is  about  one-sixth  less  than 
actual  observation  had  proved  the  velocity  to  be,  and  the 
most  curious  suppositions  were  made  to  account  for  the  dis- 
crepancy. Newton  himself  threw  out  the  conjecture  that  it 
was  only  in  passing  from  particle  to  particle  of  the  air  that 
sound  required  time  for  its  transmission;  that  it  moved 
instantaneously  through  the  particles  themselves.  He  then 
supposed  the  line  along  which  sound  passes  to  be  occupied 
by  air-particles  for  one-sixth  of  its  extent,  and  thus  he  sought 
to  make  good  the  missing  velocity.  The  very  art  and 
ingenuity  of  this  assumption  were  sufficient  to  ensure  its 
rejection ;  other  theories  were  therefore  advanced,  but  the 
great  French  mathematician  Laplace  was  the  first  to  com- 
pletely solve  the  enigma.  I  shall  now  endeavour  to  make 
you  thoroughly  acquainted  with  his  solution. 

*  I  hold  in  my  hand  a  strong  cylinder  of  glass,  accurately 
bored,  and  quite  smooth  within.  Into  this  cyhnder,  which 
is  closed  at  the  bottom,  fits  this  air-tight  piston.  By  pushing 
the  piston  down,  I  condense  the  air  beneath  it ;  and,  when  I 
do  so,  heat  is  developed.  Attaching  a  scrap  of  amadou  to  the 
bottom  of  the  piston,  I  can  ignite  it  by  the  heat  generated  by 


l82 


INDUCTIVE  METHODS. 


compression.  Dipping  a  bit  of  cotton  wool  into  bisulphide 
of  carbon,  and  attaching  it  to  the  piston,  when  the  latter  is 
forced  down,  a  flash  of  light,  due  to  the  ignition  of  the  bisul- 
phide of  carbon  vapour,  is  observed  within  the  tube.  It  is 
thus  proved  that,  when  air  is  compressed,  heat  is  generated. 
By  another  experiment,  I  can  show  you  that,  when  air  is 
rarefied,  cold  is  developed.  This  brass  box  contains  a 
quantity  of  condensed  air.  I  open  the  cock,  and  permit  the 
air  to  discharge  itself  against  a  suitable  thermometer  ;  the 
sinking  of  the  instrument  declares  the  chilling  of  the  air. 

'  All  that  you  have  heard  regarding  the  transmission  of  a 
sonorous  pulse  through  air,  is,  I  trust,  still  fresh  in  your 
minds.  As  the  pulse  advances,  it  squeezes  the  particles  of  air 
together,  and  two  results  follow  from  this  compression  of  the 
air.  Firstly,  its  elasticity  is  augmented  through  the  mere 
augmentation  of  its  density.  Secondly,  its  elasticity  is  aug- 
mented by  the  heat  developed  by  compression.  It  was  the 
change  of  elasticity  which  resulted  from  a  change  of  density 
that  Newton  took  into  account,  and  he  entirely  overlooked 
the  augmentation  of  elasticity  due  to  the  second  cause  above 
mentioned.  Over  and  above,  then,  the  elasticity  involved  in 
Newton's  calculation,  we  have  an  additional  elasticity  due  to 
changes  of  temperature  produced  by  the  sound  itself.  When 
both  are  taken  into  account,  the  calculated  and  the  observed 
velocity  agree  perfectly '^V 

It  is  not  necessary,  for  our  purposes,  to  pursue  the 
quotation,  but  the  student,  who  wishes  to  see  an  ex- 
ample of  the  extreme  delicacy  and  caution  with  which 
it  is  requisite  to  conduct  physical  researches,  may  with 
great  advantage  read  the  remainder  of  the  chapter. 

^'  lectures  on  Sound,  ch.  i. 


METHOD   OF  CONCOMITANT  VARIATIONS.     1 83 
METHOD  OF  CONCOMITANT  VARIATIONS. 


CANON. 

Whatever  phenomenon  varies  in  any  manner  whenever 
another  phenomenon  varies  in  some  particular  manner,  ts 
either  a  cause  or  an  effect  of  that  phenomenon,  or  is  con- 
nected ivith  it  through  some  fact  of  causation  ^^. 

This  Method  is  really  a  peculiar  application,  or  series 
of  applications,  of  the  Method  of  Difference.     It  is  em- 
ployed in  those  cases  where  a  phenomenon  cannot  be 
made  to  disappear  altogether,  but  where  we  have  the 
power  of  augmenting  or  diminishing  its  quantity,  or  at 
least  where    Nature   presents    it   in   greater   or  smaller 
amounts.     Thus,  suppose  we  drop  a  quantity  of  quick- 
silver into  a  glass  tube,  we  shall  find  that  every  sensible 
augmentation   of  the   temperature   of  the   surrounding 
atmosphere  is  accompanied  by  a  sensible  augmentation 
of  the  volume  of  the  quicksilver  in  the  tube,  and,  vice 
versa,  that  every  sensible  diminution  of  the  tempera- 
ture  is  accompanied  by  a  sensible  diminution  of  the 
volume   of  the   quicksilver.     Now   each   particular   ex- 
periment is  an  application  of  the  Method  of  Difference, 
and,  providing  we  have  ascertained  that  the  conditions 
of  that  Method  have  been  rigorously  satisfied,  partakes 
of  its  cogency.     That  certain  definite  augmentations  of 
temperature  will  increase  the  volume  of  quicksilver  by, 
say,  one-twentieth,  one-thirtieth,  or  one-fiftieth  part,  is  an 

♦0  On  p.  186  will  be  found  a  rider  to  this  Canon. 


1 84 


INDUCTIVE  METHODS. 


absolutely  certain  inference,  supposing  due  care  to  have 
been  taken  in  the  performance  of  the  experiments,  and 
is  simply  a  result  of  the  Method  of  Difference.  But, 
inasmuch  as  there  are  limits  above  and  below  which  we 
cannot  try  the  experiment,  or  intermediate  points  of 
temperature  at  which  we  do  not  find  it  convenient  to 
do  so,  the  question  arises  whether  we  are  justified,  in 
virtue  of  the  experiments  already  tried,  in  asserting  that 
the  volume  of  the  quicksilver  will  invariably  expand  or 
contract  in  proportion  to  the  increasing  or  diminishing 
temperature  of  the  surrounding  media.  We  are  justified 
in  making  such  an  assertion,  and  for  this  reason.  The 
cause  which  occasions  the  quicksilver  to  expand  or  con- 
tract at  two  definite  points  must,  if  it  continue  to  act, 
and  if  it  be  counteracted  by  no  other  cause,  operate  at 
all  intermediate  points ;  and,  similarly,  the  cause  which 
occasions  it  to  expand  or  contract  up  to  a  certain  point 
must,  on  the  same  suppositions,  go  on  producing  a  like 
effect.  This  fact  is  implied  in  the  very  notion  of 
Causation.  We  arrive,  then,  at  the  conclusion  that  the 
volume  of  the  quicksilver  is  invariably  dependent  on 
the  temperature  of  the  surrounding  medium ;  in  other 
words,  that  augmentation  of  temperature  is  the  cause  of 
its  expansion  *^. 

It  may  be  asked.  Why  not  employ  the  Method  of 

"  The  student  acquainted  with  the  phraseology  of  Mathematics 
will  understand  my  meaning,  when  I  say  that  the  Method  of  Con- 
comitant Variations  is  really  an  integration  of  a  (supposed;  infinite 
number  of  applications  of  the  Method  of  Difference. 


METHOD   OF  CONCOMITANT  VARIATIONS.     185 

Difference  once  and  for  all  ?  Because,  ex  hypothesi,  the 
phenomenon  is  one  which  is  only  capable  of  augmenta- 
tion or  diminution,  and  cannot  be  made  to  vanish.  We 
may  reduce  to  a  minimum  the  resistance  to  motion,  but 
we  cannot  remove  the  resistance  altogether.  We  may 
more  and  more  diminish  the  heat  of  a  body,  but  we 
cannot  wholly  deprive  the  body  of  its  heat.  Hence  we 
can  apply  the  Method  of  Difference  to  the  several  aug- 
mentations and  diminutions  of  the  phenomenon,  but  we 
cannot  apply  it  to  the  phenomenon  as  a  whole. 

In  the  example  given  above,  we  know  that  augmenta- 
tion of  temperature  and  augmentation  of  volume  are 
related  as  cause  and  effect,  because,  in  the  experiments, 
we  can  assure  ourselves  that  they  are  the  only  two  cir- 
cumstances which  vary  in  common ;  if  we  were  not 
certain  of  this  fact,  there  might  be  some  third  circum- 
stance which  was  the  cause  of  both.  Moreover,  we  know 
that  augmentation  of  temperature  is  the  cause  and  aug- 
mentation of  volume  the  effect,  because,  in  this  case,  the 
former  is  the  antecedent  and  the  latter  the  consequent. 
There  is  another  class  of  cases  where,  though  we  are  not 
able  to  determine  which  of  two  circumstances  is  cause 
and  which  is  effect,  we  may  regard  the  relation  as  being 
one  of  cause  and  effect,  inasmuch  as  we  feel  confident 
that  there  is  present  no  third  circumstance  varying  pro- 
portionately with  the  other  two.  But,  if  we  cannot  be 
confident  even  of  this  fact,  the  two  circumstances  may, 
for  aught  we  know,  both  be  effects  of  the  same  cause ; 
as,  for  instance,  the  loudness  of  a  clap  of  thunder  varies 


i86 


INDUCTIVE  METHODS. 


with  the  intensity  of  a  flash  of  lightning,  though  neither 
is  the  cause  of  the  other,  both  ahke  being  effects  of  the 
electrical  condition  of  the  atmosphere.  Hence  will  be 
seen  the  importance  of  the  concluding  words  of  the 
Canon,  'or  is  connected  with  it  through  some  fact  of 
causation.'  The  first  and  second  cases  differ  from  the 
third  in  this,  that  in  both  of  them  we  suppose  a  rigorous 
fulfilment  of  the  requisitions  of  the  Method  of  Difference 
as  applied  to  those  individual  observations  or  experi- 
ments on  which  the  Method  of  Concomitant  Variations 
is  founded,  and  which  it,  as  it  were,  sums  up.  In  the 
last  case,  however,  we  suppose  that  there  is  some  un- 
certainty as  to  whether  the  requisitions  of  the  Method  of 
Difference  have  been  rigorously  fulfilled  or  not.  It  will 
thus  be  seen  that  the  statement  of  the  Canon,  as  given 
above,  is  adapted  to  the  weakest  case.  I  may  add  to  it 
the  following  rider  : — 

If  we  can  assure  ourselves  that  there  is  no  third  pheno- 
menon varying  concurrently  with  these  two^  we  may  affirm 
that  the  one  phe?iomenon  is  either  the  cause  or  the  effect  of 
the  other. 

The  Method  of  Concomitant  Variations  may  be  used 
for  two  purposes,  either  to  establish  a  causal  connexion, 
or  to  determine  the  law  according  to  which  two  pheno- 
mena vary.  Thus,  it  may  either  establish  the  fact  that 
any  increase  of  temperature  causes  quicksilver  to  expand, 
or  it  may  determine  the  exact  rate  according  to  which 
this  expansion  takes  place,  a  determination  which  is,  in 
fact,  effected  by  the  ordinary  thermometer.     In  the  latter 


METHOD   OF  CONCOMITANT  VARIATIONS.     187 

case,  the  application  of  the  Method  is  not  confined  to 
those  permanent  natural  agents  referred  to  above,  the 
influence  of  which  we  cannot  altogether  remove  ;  it  may 
come  in  as  supplementary  to  the  Method  of  Difference. 
Thus  it  is  by  the  Method  of  Difference  that  we  discover 
that  certain  kinds  of  impurity  in  the  atmosphere  produce 
certain  kinds  of  disease,  but,  if  we  could  ascertain  the 
relation  subsisting  between  the  amount   of  impurity  in 
the  atmosphere  and  the  amount  of  disease,  it  would  be  by 
an  application  of  the  Method  of  Concomitant  Variations. 
In  the  latter  class  of  enquiries,  the  attempt  to  deter- 
mine the    numerical    relations   according  to  which  two 
phenomena  vary,  the  utmost  caution  is  required  as  soon 
as  our  inference  outsteps  the  limits  of  our  observations. 
In  the  first  place,  there  is  always  the  possibility  of  the 
intervention  of  some  counteracting  cause.     In  the  case 
of  water,  we  found  that,  at  39',  instead  of  continuing  to 
contract  as  it  becomes  colder,  it  ceases  at  that  point  to 
do  so,  and  thenceforward  begins  to  expand.     '  No  coun- 
teracting cause  intervening '  is,  however,  a  qualification 
with  which  we  must  understand  all  our  inductions,  by 
whatever  method  they  may  have  been  arrived  at.     But 
there  is  an  element  of  uncertainty  which  is  peculiar  to 
the    Method  of  Concomitant  Variations   as   applied  to 
determine   the   laiv  or   rate   of  variation    between  two 
phenomena,  especially  when  the  range  of  our  observations 
is  confined  within   comparatively  narrow  limits.     *Any 
one,'  says  Mr.  Mill'-,  'who  has  the  slightest  acquaint- 
"  Mill's  Logic,  Bk.  III.  ch.  viii.  §  7. 


i88 


INDUCTIVE  METHODS, 


m 


ance  with  mathematics,  is  aware  that  very  different  laws 
of  variation  may  produce  numerical  results  which  differ 
but  slightly  from  one  another  within  narrow  limits  ;  and 
it  is  often  only  when  the  absolute  amounts  of  variation 
are  considerable,  that  the  difference  between  the  results 
given  by  one  law  and  by  another  becomes  appreciable. 
When,  therefore,  such  variations  in  the  quantity  of  the 
antecedents  as  we  have  the  means  of  observing  are  small 
in  comparison  with    the  total  quantities,  there  is  much 
danger  lest  we  should  mistake  the  numerical  law,  and 
be  led  to  miscalculate  the  variations  w^hich  would  take 
place  beyond  the  limits  \  a  miscalculation  which  would 
vitiate  any  conclusion  respecting  the  dependence  of  the 
effect  upon  the  cause,  that  could  be  founded  on  those 
variations.     Examples  are  not  wanting  of  such  mistakes. 
"The  formulae,"  says  Sir  John   Herschel,  "which  have 
been  empirically  deduced  for  the  elasticity  of  steam  (till 
very  recently),  and   those  for  the   resistance   of  fluids, 
and  other  similar  subjects,"  when  relied  on  beyond  the 
limits  of  the  observations  from  which  they  were  deduced, 
"  have  almost  invariably  failed  to  support  the  theoretical 
structures  which  have  been  erected  on  them.'"     This, 
how^ever,  it  must  be  noticed,  is  an  uncertainty  which  does 
not  vitiate  the  method,  but  simply  renders  necessary  the 
exercise  of  the  utmost  caution  in  its  application. 

Perhaps  no  simpler  instance  of  the  Method  of  Con- 
comitant Variations  can  be  given  than  the  experimental 
proof  of  the  First  Law  of  Motion,  which  Law  may  be 
stated  thus :  that  all  bodies  in  motion  continue  to  move 


METHOD  OF  CONCOMITANT  VARIATIONS,     1 89 

in  a  straight  line  with  uniform  velocity  until  acted  upon 
by  some  new  force. 

*  This  assertion,'  I  am  quoting  from  Mr.  Mill*^  '  is  in  open 
opposition  to  first  appearances  ;  all  terrestrial  objects,  when 
in  motion,  gradually  abate  their  velocity  and  at  last  stop; 
which    accordingly  the    ancients,    with    their   inductio  per 
enumerationem  simpHcem,  imagined  to  be  the  law.    Every 
moving   body,   however,   encounters    various   obstacles,   as 
friction,  the  resistance    of   the    atmosphere,  &c.,  which  we 
know  by  daily  experience  to  be  causes  capable  of  destroying 
motion.     It  was  suggested  that  the  whole  of  the  retardation 
might  be  owing  to  these  causes.      How  was  this  enquired 
into?    If  the  obstacles  could  have  been  entirely  removed,  the 
case  would  have  been  amenable  to  the  Method  of  Difference. 
They  could  not  be  removed,  they  could  only  be  diminished, 
and   the   case,  therefore,  admitted   only  of  the  Method  of 
Concomitant  Variations.     This  accordingly  being  employed, 
it  was  found  that  every  diminution  of  the  obstacles  diminished 
the  retardation  of  the  motion  :  and,  inasmuch  as  in  this  case 
(unlike  the  case  of  heat)  the  total  quantities   both   of  the 
antecedent  and  of  the  consequent  were  known,  it  was  prac- 
ticable to  estimate,  with  an  approach  to  accuracy,  both  the 
amount  of  the  retardation  and  the  amount  of  the  retarding 
causes  or  resistances,  and  to  judge  how  near  they  both  were 
to  being  exhausted;  and  it  appeared  that  the  effect  dwindled 
as  rapidly  [as  the  cause],  and  at  each  step  was  as  far  on  the 
road  towards  annihilation   as  the   cause  was.     The  simple 
oscillation   of  a  weight  suspended  from  a  fixed  point,  and 
moved  a  little  out  of  the  perpendicular,  which  in  ordinary 
circumstances   lasts   but    a   few  minutes,  was  prolonged  in 
Borda's  experiments  to  more  than  thirty  hours,  by  diminishing 
as  much  as  possible  the  friction  at  the  point  of  suspension, 
and  by  making  the  body  oscillate  in  a  space  exhausted  as 


43 


Mill's  Logic,  Bk.  III.  ch.  viii.  §  7. 


190 


INDUCTIVE  METHODS, 


nearly  as  possible  of  its  air.  There  could  therefore  be 
no  hesitation  in  assigning  the  whole  of  the  retardation  of 
motion  to  the  influence  of  the  obstacles  :  and  since,  after 
subducting  this  retardation  from  the  total  phenomenon,  the 
remainder  was  an  uniform  velocity,  the  result  was  the  pro- 
position known  as  the  first  law  of  motion.' 

I  have  already  employed  as  an  illustration  the  fact 
that  a  change  in  the  temperature  of  a  body  is  always 
accompanied  by  a  change  in  its  volume.  The  following 
extract  places  the  same  fact  in  a  new  light,  and  shows 
that  the  nature  of  substance  (whether  solid,  liquid,  or 
aeriform)  depends  on,  and,  at  considerable  intervals, 
varies  with,  the  temperature  to  which  it  is  exposed. 

*  The  most  striking  and  important  of  the  effects  of  heat 
consist,  however,  in  the  liquefaction  of  solid  substances,  and 
the  conversion  of  the  liquids  so  produced  into  vapour.  There 
is  no  solid  substance  known  which,  by  a  sufficiently  intense 
heat,  may  not  be  melted,  and  finally  dissipated  in  vapour ; 
and  this  analogy  is  so  extensive  and  cogent,  that  we  cannot 
but  suppose  that  all  those  bodies,  which  are  liquid  under 
ordinary  circumstances,  owe  their  liquidity  to  heat,  and 
would  freeze  or  become  solid  if  their  heat  could  be  sufficiently 
reduced.  In  many  we  see  this  to  be  the  case  in  ordinary 
winters  ;  for  some,  severe  frosts  are  requisite  ;  others  freeze 
only  with  the  most  intense  artificial  colds;  and  some  have 
hitherto  resisted  all  our  endeavours  :  yet  the  number  of 
these  last  is  few,  and  they  will  probably  cease  to  be  excep- 
tions as  our  means  of  producing  cold  become  enlarged. 

*  A  similar  analogy  leads  us  to  conclude  that  all  aeriform 
fluids  are  merely  liquids  kept  in  the  state  of  vapour  by  heat. 
Many  of  them  have  been  actually  condensed  into  the  liquid 
state  by  cold  accompanied  with  violent  pressure  ;  and,  as  our 
means  of  applying  these  causes  of  condensation  have  im- 


METHOD   OF  CONCOMITANT  VARIATIONS,     19I 


proved,  more  and  more  refractory  ones  have  successively 
yielded.  Hence  we  are  fairly  entitled  to  extend  our  con- 
clusion to  those  which  we  have  not  yet  been  able  to  succeed 
with  ;  and  thus  we  are  led  to  regard  it  as  a  general  fact,  that 
the  liquid  and  aeriform  or  vaporous  states  are  entirely 
dependent  on  heat;  that,  were  it  not  for  this  cause,  there 
would  be  nothing  but  solids  in  nature;  and  that,  on  the 
other  hand,  nothing  but  a  sufficient  intensity  of  heat  is 
requisite  to  destroy  the  cohesion  of  every  substance,  and 
reduce  all  bodies,  first  to  liquids,  and  then  into  vapour".' 

An  interesting  application  of  the  Method  of  Concomi- 
tant Variations  is  found  in  the  arguments  by  which  it 
is  established  that  refrigeration  at  night  (when  the  sun's 
rays  are  withdrawn)  is,  cceteris  paribus^  proportional  to 
the  dryness  of  the  atmosphere.  Thus,  in  the  British 
Isles,  where  the  atmosphere  almost  always  contains  a 
large  amount  of  aqueous  vapour,  the  difference  between 

**  Herschel's  Discourse  on  the  Study  of  Natural  Philosophy,  §§ 

357»  358. 

Sir  John  Herschel's  conjecture  has  been  verified  with  regard  to 

aeriform  fluids,  and  is  now  rapidly  in  course  of  being  verified  with 
regard  to  liquids.  The  experiments  of  Cailletet  and  Pictet  (an 
account  of  which  may  be  found  in  the  Academy  of  Jan.  12th,  1878, 
and  in  Nature  of  Jan.  3rd  and  1 7th  of  the  same  year)  have  conclusively 
shown  that  even  oxygen,  hydrogen,  and  nitrogen  admit  of  liquefac- 
tion. Thus,  the  old  distinction  between  permanent  and  non-per- 
manent gases  has  been  entirely  effaced.  And  the  application  of 
the  very  low  temperature  which  can  now  be  so  readily  procured  has 
lessened  the  nllmber  of  those  liquids  which,  till  quite  recently,  it  was 
thought  could  not  be  solidified.  For  example,  it  has  been  observed 
that  disulphide  of  carbon  solidifies  at  —  116°  and  fuses  again  at 
about  —  1 10*^,  that  pure  ether  solidifies  at  —  129°,  and  absolute 
alcohol  becomes  viscid  at  —  129°  and  solidifies  at  —  130-5°.  See 
Ganot's  Physics,  13th  ed.  §  343. 


192 


INDUCTIVE  METHODS, 


the  temperature  at  day  and  night  is  comparatively  slight, 
whereas,  in  countries  far  inland,  where  the  atmosphere  is 
extremely  dry,  the  variations  of  temperature  are  compara- 
tively large.  This  phenomenon  is  due  to  the  fact  that 
masses  of  aqueous  vapour,  though  they  intercept,  also 
radiate  heat.  Hence,  while  during  the  day  they  protect 
us  from  the  excessive  heat  of  the  sun,  they  intercept  the 
heat  which  is  radiated  from  the  earth's  surface  during 
the  night,  and,  at  the  same  time,  return  to  it  some  por- 
tion of  the  heat  they  have  absorbed  during  the  day. 

<  A  freedom  of  escape,'  says  Professor  Tyndall  *^  *  would 
occur  at  the  earth's  surface  generally,  were  the  aqueous 
vapour  removed  from  the  air  above  it,  for  the  great  body 
of  the  atmosphere  is  a  practical  vacuum,  as  regards  the 
transmission  of  radiant  heat.  The  withdrawal  of  the  sun 
from  any  region  over  which  the  atmosphere  is  dry,  must  be 
followed  by  quick  refrigeration.  The  moon  would  be  ren- 
dered entirely  uninhabitable  by  beings  like  ourselves  through 
the  operation  of  this  single  cause  ;  with  a  radiation,  uninter- 
rupted by  aqueous  vapour,  the  difference  between  her  monthly 
maxima  and  minima  must  be  enormous.  The  winters  of 
Thibet  are  almost  unendurable,  from  the  same  cause.  Witness 
how  the  isothermal  lines  dip  from  the  north  into  Asia,  in 
winter,  as  a  proof  of  the  low  temperature  of  this  region. 
Humboldt  has  dwelt  upon  the  "frigorific  power"  of  the 
central  portions  of  this  continent,  and  controverted  the  idea 
that  it  was  to  be  explained  by  reference  to  the  elevation; 
there  being  vast  expanses  of  country,  not  mucTi  above  the 
sea-level,  with  an  exceedingly  low  temperature.  But,  not 
knowing  the  influence  which  we  are  now  studying,  Humboldt, 
I  imagine,  omitted  the  most  potent  cause  of  the  cold.    The 

«  T)  ml  all's  Heat  a  Mode  of  Motion,  §  492. 


METHOD   OF  CONCOMITANT  VARIATIONS,    1 93 

refrigeration  at  night  is  extreme  when  the  air  is  dry.  The 
removal,  for  a  single  summer  night,  of  the  aqueous  vapour 
from  the  atmosphere  which  covers  England,  would  be 
attended  by  the  destruction  of  every  plant  which  a  freezing 
temperature  could  kill.  In  Sahara,  where  "  the  soil  is  fire 
and  the  wind  is  flame,"  the  cold  at  night  is  often  painful  to 
bear.  Ice  has  been  formed  in  this  region  at  night.  In 
Australia,  also,  the  diurnal  range  of  temperature  is  very- 
great,  amounting,  commonly,  to  between  40  and  50  degrees. 
In  short,  it  may  be  safely  predicted  that,  wherever  the  air  is 
dry^  the  daily  thermometric  range  will  be  great.  This,  how- 
ever, is  quite  different  from  saying  that,  where  the  air  is  dear, 
the  thermometric  range  will  be  great.  Great  clearness  to 
light  is  perfectly  compatible  with  great  opacity  to  heat  ;  the 
atmosphere  may  be  charged  with  aqueous  vapour  while 
a  deep  blue  sky  is  overhead,  and  on  such  occasions  the 
terrestrial  radiation  would,  notwithstanding  the  *'  clearness," 
be  intercepted.' 


The  science  of  Geology  abounds  in  instances  of  the 
employment  of  the  Method  of  Concomitant  Variations. 
In  fact,  as  the  agents  with  which  it  is  concerned,  land 
and  water,  subsidence  and  elevation,  deposition  and 
denudation,  are  constantly  present  and  acting  on  the 
earth's  surface,  and  as  it  is  impossible  to  cause  the 
influence  of  any  one  of  them  to  vanish  altogether,  the 
geologist  is  compelled  in  his  explanations  and  arguments 
to  avail  himself  mainly  of  this  method.  The  following 
extract  from  Lyell's  Principles  of  Geology  furnishes  a 
good  illustration,  and  will  be  peculiarly  interesting  to 
any  one  who  has  visited  the  place.  It  is  designed  as  an 
explanation  of  the  alternate  subsidence  and  elevation  of 

o 


194 


INDUCTIVE  METHODS, 


the  famous  temple  of  Jupiter  Serapis,  at  Pozzuoli,  on 
the  Bay  of  Naples. 

*  We  can  scarcely  avoid  the  conclusion,  as  Mr.  Babbage 
has  hinted,  "  that  the  action  of  heat  is  in  some  way  or  other 
the  cause  of  the  phenomena  of  the  change  of  level  of  the 
temple.     Its  own  hot  spring,  its  immediate  contiguity  to  the 
Solfatara,  its  nearness  to  the  Monte  Nuovo,  the  hot  spring  at 
the  baths  of  Nero  on  the  opposite  side  of  the  Bay  of  Baiae, 
the  boiling  springs  and  ancient  volcanos  of  Ischia  on  one  side 
and  Vesuvius   on    the   other,  are  the  most  prominent  of  a 
multitude   of  facts  which  point  to  that  conclusion."      And 
when  we  reflect  on  the  dates  of  the  principal  oscillations  of 
level,  and  the  volcanic  history  of  the  country  before  described, 
we    seem   to   discover   a   connexion   between   each   era    of 
upheaval  and  a  local  development  of  volcanic  heat,  and  again 
between  each  era  of  depression  and  the   local   quiescence 
or  dormant   condition  of  the  subterranean  igneous  causes. 
Thus  for  example,  before  the  Christian  era,  when  so  many 
vents  were  in  frequent  eruption  in  Ischia,  and  when  Avernus 
and  other  points  in  the  Phlegncan  Fields  were  celebrated  for 
their  volcanic  aspect  and  character,  the  ground  on  which  the 
temple  stood  was  several  feet  above  water.    Vesuvius  was 
then    regarded   as   a   spent   volcano ;   but   when,   after  the 
Christian  era,  the   fires   of  that  mountain  were   rekindled, 
scarcely  a  single   outburst    was   ever   witnessed   in    Ischia, 
or  around  the  Bay  of  Baia?.     Then  the  temple  was  sinking. 
Vesuvius,  at  a  subsequent  period,  became  nearly  dormant  for 
five  centuries  preceding  the  great  outbreak  of  1 631,  and  in 
that  interval  the  Solfatara  was  in  eruption  A.D.  1 198,  Ischia 
in  1302,  and  Monte  Nuovo  was  formed  in  1538.     Then  the 
foundations  on  which  the  temple  stood  were  rising  again. 

Lastly,  Vesuvius  once  more  became  a  most  active  vent,  and 
has  been  so  ever  since,  and  during  the  same  lapse  of  time  the 
area  of  the  temple,  so  far  as  we  know  anything  of  its  history, 

has  been  subsiding. 


METHOD   OF  CONCOMITANT  VARIATIONS,     195 

*  These  phenomena  would  agree  well  with  the  hypothesis, 
that  when  the  subterranean  heat  is  on  the  increase,  and  when 
lava  is  forming  without  obtaining  an  easy  vent,  like  that 
afforded  by  a  great  habitual  chimney,  such  as  Vesuvius,  the 
incumbent  surface  is  uplifted,  but  when  the  heated  rocks 
below  are  cooling  and  contracting,  and  sheets  of  lava  are 
slowly  consolidating  and  diminishing  in  volume,  then  the 
incumbent  land  subsides  *^.' 

Laplace's  Nebular  Hypothesis,  that  stellar  systems,  like 
our  solar  system,  are  formed  from  the  gradual  condensa- 
tion of  nebular  masses,  is  supported  by  an  appeal  to 
this  method.  *  We  see,'  conceives  Laplace,  *  among  these 
nebulae '  (which  are  diffused  along  the  Milky  Way),  '  in- 
stances of  all  degrees  of  condensation,  from  the  most 
loosely  diffused  fluid,  to  that  separation  and  solidification 
of  parts  by  which  suns  and  satellites  and  planets  are 
formed  :  and  thus  we  have  before  us  instances  of  systems 
in  all  their  stages  ;  as  in  a  forest  we  see  trees  in  every 
period  of  growth  *"^.' 

Physiology  (so  far  as  it  is  based  on  Anatomy,  as 
distinct  from  direct  experiment),  for  like  reasons  with 
Geology,  mainly  employs  the  Method  of  Concomitant 
Variations.  It  is  very  seldom,  in  this  science,  that  we 
obtain  a  phenomenon   present   in  one  set  of  instances 

<•  Lyell's  Principles  of  Geology y  tenth  edition,  ch.  xxx. 

*^  Whewell's  Novum  Qrganon  Kenovatum^  Bk.  III.  ch.  viii.  sect. 
2.  §  9.  This  example  is  adduced  by  Dr.  Whewell  as  an  instance  of 
what  he  calls  the  Method  of  Gradation,  which,  however,  must  not 
be  confounded  with  MilFs  Method  of  Concomitant  Variations.  The 
example,  so  far  as  it  can  be  relied  on,  serves  equally  well  as  an 
instance  of  either  method. 

O  2 


196  INDUCTIVE  METHODS. 

and  entirely  absent  in  another  ;  but  we  frequently  find  a 
phenomenon  which,  within  certain  limits,  presents  itself 
in  the  most  variable  quantities.  If,  then,  we  find  another 
phenomenon  varying  as  it  varies,  we  may  argue  with 
tolerable  confidence  that  the  two  phenomena  either  stand 
to  each  other  in  the  relation  of  cause  and  effect,  or  are,  at 
least,  common  effects  of  some  unknown  cause.  Thus,  it 
appears  to  be  established  that,  not  only  in  different 
species,  but  in  different  individuals  of  the  same  species, 
there  is  some  relation  between  the  manifestations  of  in- 
telligence and  the  amount  of  cerebral  development,  under- 
standing the  latter  expression  to  include  not  only  bulk  of 
brain  but  also  complexity  and  depth  of  convolutions. 

*  With  some  apparent  exceptions,'  says  Dr.  Carpenter  *^  a 
classical  authority  on  most  physiological  questions,  '  which 
there  would  probably  be  no  great  difficulty  in  explaining 
if  we  were  in  possession  of  all  the  requisite  data,  there  is  a 
very  close  correspondence  between  the  relative  development 
of  the  Cerebrum  in  the  several  tribes  of  Vertebrata  and  the 
degree  of  Intelligence  they  respectively  possess— using  the 
latter  term  as  a  comprehensive  expression  for  that  series  of 
mental  actions  which  consists  in  the  in/e?tiional  adaptation 
of  means  to  ends,  based  on  definite  ideas  as  to  the  nature 
of  both.' 

And  again  : — 

'  As  we  ascend  the  Mammalian  series,  we  find  the  Cere- 
brum becoming  more  and  more  elongated  posteriorly  by  the 
development  of  the  middle  lobes,  and  the  intercerebral  con- 
missure  becomes  more  complete;  but  we  must  ascend  as 

*"  Carpenter's  Principles  of  Human  Physiolo^,  sixth  edition, 
1 S64. 


METHOD   OF  CONCOMITANT  VARIATIONS.    J 97 

high  as  the  Carnivora,  before  we  find  the  least  vestige  of  the 
posterior  lobes ;  and  the  rudiment  which  these  possess  is  so 
rapidly  enlarged  in  the  Quadrumana,  that  in  some  of  that 
group  the  posterior  lobes  are  as  fully  developed  in  reference 
to  the  Cerebrum  as  a  whole,  and  as  completely  cover  in  the 
Cerebellum,  as  in  the  human  subject.  The  attention  which 
has  yet  been  given  to  this  department  of  enquiry,  has  not 
hitherto  done  more  than  confirm  the  statement  already  made, 
with  regard  to  the  general  correspondence  between  the 
development  of  the  Cerebrum  and  the  manifestations  of 
Intelligence ;  very  decided  evidence  of  which  is  furnished 
by  the  great  enlargement  of  the  Cerebrum,  and  the  corre- 
sponding alteratioruin  the  form  of  the  Cranium,  which  present 
themselves  in  those  races  of  Dogs  most  distinguished  for 
their  educability,  when  compared  with  those  whose  con- 
dition approximates  most  closely  to  what  was  probably  their 
original  state  of  wildness. 

*  This  general  inference,  drawn  from  Comparative  Anatomy, 
is  borne  out  by  observation  of  the  human  species.  When  the 
Cerebrum  is  fully  developed,  it  offers  innumerable  diversities 
of  form  and  size  among  various  individuals  ;  and  there  are 
as  many  diversities  of  character.  It  may  be  doubted  if  two 
individuals  were  ever  exacUy  alike  in  this  respect.  That  a 
Cerebrum  which  is  greatly  under  the  average  size  is  incapable 
of  performing  its  proper  functions,  and  that  the  possessor  of 
it  must  necessarily  be  more  or  less  idiotic,  there  can  be  no 
reasonable  doubt.  On  the  other  hand,  that  a  large,  well- 
developed  Cerebrum  is  found  to  exist  in  persons  who  have 
made  themselves  conspicuous  in  the  world  in  virtue  of  their 
intellectual  achievements,  may  be  stated  as  a  proposition  of 
equal  generality.* 

Dr.  Thurnam^^,  taking  the  brain-weights  of  ten  dis- 


*»  On  the  Weight  of  the  Brain,  by  John  Thurnam,  M.D.     London, 
J.  E.  Adlard.     1866. 


198 


INDUCTIVE  METHODS, 


tinguished  men,  who  died  between  the  ages  of  fifty  and 
seventy,  calculates  the  average  weight  of  their  brains 
to  have  been  547  ounces.  The  average  weight  of  the 
brains  of  ordinary  men,  dying  between  the  same  ages, 
is  47*1  ounces.  These  facts  give  in  favour  of  '  cultivated 
and  intellectual  man'  an  excess  of  7*6  ounces,  or  15  per 
cent.  Though,  as  a  general  rule,  the  connexion  between 
intellectual  and  cerebral  development  appears  to  be  sub- 
stantiated, we  must,  however,  be  very  cautious  in  drawing 
any  inferences  as  to  particular  cases.  Megalocephaly, 
or  pathological  enlargement  of  the  brain,  is  a  recognised 
disease,  and  is  frequently  attended  with  idiotcy.  In  this 
class  of  cases,  no  doubt,  if  our  means  of  investigation 
were  adequate,  we  should  discover  some  peculiarity 
either  in  the  chemical  composition  or  in  the  anatomical 
structure  of  the  brain  which  would  enable  us  to  explain 
the  exceptions  in  conformity  with  the  rule. 

It  is,  perhaps,  needless  to  add  that  we  are  not  justified 
in  drawing  any  further  inference  from  these  data,  than  that 
the  brain  is  the  organ  of  intelhgence,  and  that  there  is 
some  definite  relation  between  the  organ  and  its  functions. 

Another  interesting  application  of  the  Method  of  Con- 
comitant Variations  may  be  found  in  one  of  the  argu- 
ments by  which  the  distinction  between  Formed  and 
Germinal  Material  is  established.  Any  piece  of  glandular 
tissue,  if  examined  under  a  microscope,  will  be  found 
to  consist  of  two  parts,  one  of  which  will  take  a  tint 
from  carmine,  the  other  not.  The  portion  which  takes 
the  tint  is  called  Germinal,  the  portion  which  will  not 


METHOD   OF  COAXOMITANT  VARIATIONS.     1 99 

take  it  is  called  Formed  Material.  The  former  is  living 
matter,  capable  of  growth  and  germination;  the  latter 
is  dead  matter,  capable  of  no  change  but  decay.  Now, 
if  this  distinction  between  the  two  kinds  of  matter  be 
well  founded,  we  may  reasonably  expect  to  find  the  ger- 
minal matter  developed  in  much  larger  proportions  in 
the  younger  than  in  the  older  specimens  of  animals  and 
plants,  and  in  what  may  be  called  the  more  active  than 
in  what  may  be  called  the  more  passive  parts  of  animal 
and  vegetable  organisms.  And  this  is  the  case.  In  the 
pith  of  rush,  elder,  &c.  we  find  that,  in  the  spring,  there 
are  many  portions  of  the  cells  which  will  take  the  car- 
mine tint ;  in  summer,  few ;  in  autumn,  none.  In  the 
crystalline  lens  of  the  eyes  of  young  animals  the  portions 
which  will  take  it  preponderate,  becoming  proportionately 
fewer  as  we  examine  the  eyes  of  older  specimens.  In 
the  grey  matter  of  the  brain  we  find  many  parts  which 
will  take  the  carmine  tint,  in  the  white  matter  but  few. 
In  a  grain  of  wheat,  when  formed,  there  is,  in  the  peri- 
sperm,  no  portion  which  will  take  it,  in  the  white  matter 
but  a  small  portion,  while  in  the  embryo  it  is  often 
difficult  to  discover  any  part  which  does  not  take  it. 
These  instances  might  be  multiplied  to  any  extent  ^^ 

In  physiological  and  medical  researches,  we  must  be 
peculiarly  careful  to  bear  in  mind  that,  though  two  pheno- 
mena may  vary  proportionately,  it  by  no  means  follows 

^  The  student  will  find  this  subject  fully  treated  in  Dr.  Lionel 
Beale's  Lectures  on  the  Simple  Tissue  of  the  Human  Body^  and  in 
other  works  of  the  same  author. 


200 


INDUCTIVE  METHODS, 


that  one  is  cause  and  the  other  effect.  They  may  both 
be  common  effects  of  the  same  cause.  Thus,  though  the 
prevalence  of  some  disease  might  be  constantly  attended 
by  the  appearance  of  certain  low  forms  of  organic  life, 
such  as  what  we  now  call  microbes,  it  would  by  no  means 
follow  that  these  microbes  were  the  cause  of  the  disease, 
unless,  by  direct  experiment  on  healthy  organisms,  we 
could  establish  that,  all  other  circumstances  remaining 
the  same,  the  introduction  of  the  microbe  was  followed 
by  the  appearance  of  the  disease. 

The  Method  of  Concomitant  Variations  is  that  which 
is  most  frequently  employed  in  the  Science  of  Language. 
It  is  found,  for  instance,  that  between  two  dissimilar  words 
employed  at  different  epochs  to  express  the  same  idea 
may  be  interpolated  a  number  of  intermediate  forms 
employed  at  intermediate  epochs,  which  make  the  tran- 
sition from  the  one  word  to  the  other  gradual  and 
natural.  P>om  this  circumstance  it  is  inferred  that  the 
word  used  at  the  later  epoch  is  derived  from  that  used 
at  the  earlier  epoch,  certain  tendencies  of  speech  being 
regarded  as  the  cause  of  the  divergence.  *  Thus,  at  first 
sight,'  says  M.  Brachet  ^\  '  it  is  hard  to  see  that  d))ie  is 
derived  from  anima  ;  but  history,  our  guiding-line,  shows 
us  that  in  the  thirteenth  century  the  word  was  written 
anme^  in  the  eleventh  aneme^  in  the  tenth  anittie^  which 
leads  us  straight  to  the  Latin  animal  In  this  case  there 
can  be  no  doubt  of  the  truth  of  the  conclusion. 

""'^  M.  Brachet's  His  tori cal  Grammar  of  the  French  Tongue,  Dr. 
Kitchin's  Translation,  p.  42.     Seventh  Edition,  p.  53. 


METHOD   OF  CONCOMITANT  VARIATIONS,    201 

Similarly,  the  loss  of  declension  in  the  transition  from 
the  Latin  Language  to  the  French  is  easily  explained 
when  we  take  into  account  the  following  considera- 
tions : — 

'  The  tendency  to  simplify  and  reduce  the  number  of  cases 
was  early  felt  in  the  popular  Latin:  the  cases  expressed 
shades  of  thought  too  delicate  and  subtle  for  the  coarse  mind 
of  the  Barbarian.  And  so,  being  unable  to  handle  the  learned 
and  complicated  machinery  of  the  Latin  declensions,  he  con- 
structed a  system  of  his  own,  simplifying  its  springs,  and 
reducing  the  number  of  the  effects  at  the  price  of  frequently 
reproducing  the  same  form.  Thus  the  Roman  distinguished 
by  means  of  case-terminations  the  place  where  one  is,  from 
the  place  to  which  one  is  going  :  "  veniunt  ad  domum," 
"  sunt  in  domo."  But  the  Barbarian,  unable  to  grasp  these 
finer  shades,  saw  no  use  in  this  distinction,  and  said,  in 
either  case  alike,  **  sum  in  domum,"  '*  venio  ad  domum." 

*  Thus,  from  the  fifth  century  downwards,  long  before  the 
first  written  records  of  the  French  language,  popular  Latin 
reduced  the  number  of  cases  to  two:  (i)  the  nominative  to 
mark  the  subject;  and  (2)  that  case  which  occurred  most 
frequently  in  conversation,  the  accusative,  to  mark  the  object 
or  relation.  From  that  time  onwards  the  Latin  declension 
was  reduced  to  this  :— subject,  miirus;  object,  murwit. 

*  The  French  language  is  the  product  of  the  slow  develop- 
ment of  popular  Latin  ;  and  French  grammar,  which  was 
originally  nothing  but  a  continuation  of  the  Latin  grammar, 
inherited,  and  in  fact  possessed  from  its  infancy,  a  com- 
pletely regular  declension  :  subject,  7mirSy  viurusj  object, 
mur,  viuriim  :  and  people  said  "  ce  niurs  est  haut; "  "j'ai 
con  St  ru it  un  iniirr 

*  This  declension  in  two  cases  forms  the  exact  difference 
between  ancient  and  modern  French.  It  disappeared  in  the 
fourteenth  century,  not  without  leaving  many  traces  in  the 


202 


INDUCTIVE  METHODS, 


language,  which  look  like  so  many  insoluble  exceptions,  but 
find  their  explanation  and  historic  justification  in  our  know- 
ledge of  the  Old  French  declension  '''^.' 

Here  the  conclusion  is  that  French  Grammar  is  derived 
from  Latin  Grammar,  certain  peculiarities  of  the  period 
intervening  between  the  use  of  the  Latin  and  modern 
French  languages  being  regarded  as  the  cause  of  the 
differences  between  them. 

Again,  nothing  at  first  sight  would  appear  more  im- 
probable than  that  the  French  word  suis  and  the  Greek 
word  ftp  are  derived  from  the  same  root.  But,  when 
we  compare  the  old  French  word  siii^  the  Latin  sum^ 
the  Old  Latin  esum,  and  the  Old  Greek  form  fV/i«,  the 
connexion  of  the  two  words  and  their  ultimate  deriva- 
tion from  a  common  root  becomes  a  certainty.  Here 
the  divergence  may  be  definitely  accounted  for  by  the 
various  influences  operating  upon  people  (like  the  Latins 
and  Greeks)  occupying  different  tracts  of  country,  ex- 
posed to  different  circumstances,  having  the  organs  of 
speech  differently  modified,  and  the  like. 

Amongst  the  above  examples  it  will  be  noticed  that 
some  have  been  included,  the  conclusions  of  which  are 
by  no  means  absolutely  certain.  In  these  cases,  the 
deficiency  of  proof  is  due  not  to  any  formal  inconclusive- 
ness  in  the  Method  of  Concomitant  Variations,  or  in  that 
of  Difference,  on  which  it  is  based,  but  to  the  existence 
of  a  doubt  as  to  whether  the   requirements   of  those 

5'  M.  Brachet's  Historical  Grammar  of  the  French  Tongue,  Dr. 
Kitchin's  Translation,  p.  88.     Seventh  Edition,  pp.  98-100. 


METHOD    OF  CONCOMITANT   VARIATIONS.     203 

methods  have  been  stringently   fulfilled.     In   any   but 
the  Experimental  Sciences  it  is  always  extremely  difficult 
to  assure  ourselves  that  we  are  acquainted  with  all  the 
circumstances  which  may  influence,  or  may  be  influenced 
by,  any  given  phenomenon.     Moreover,  as  is  the  case,  for 
instance,  with  regard  to  the  concomitance  between  cere- 
bral development  and  the  manifestation  of  intelligence, 
there  may  be  many  known  points  of  difference  between 
the  observed  cases  besides  those  which  are  taken  into 
account,  and  the  value  of  the  conclusion  will  depend  on 
the  extent  to  which  we  have  ascertained  that  these  other 
points  of  difference  are  not  pertinent,  or  not  equally  perti- 
nent with  those  which  we  have  taken  into  account,  to  the 
circumstance  or  circumstances  which  we  are  investigating. 
The  application  of  the  Method  of  Concomitant  Varia- 
tions  to   determine  the   numerical   relations  subsisting 
between  two  phenomena  may  be  illustrated  from  the  ex- 
periments by  which  the  measure  of  the  accelerating  force 
of  gravity  was  established.     The  fact,  that  the  higher  the 
point  from  which  a  body  falls,  the  greater  is  the  velocity 
acquired,  is  patent  to  observation,  though,  if  we  analyse 
the  process  by  which  we  arrive  at  the  conclusion,  it  is 
by  the  Method  of  Concomitant   Variations.     The  rate 
of  acceleration,  however,  is  a  very  difficult  and  delicate 
problem  to  solve.     By  means  of  the  oscillating  pendulum 
or  Atwood's  machine  (which  it  is  unnecessary  to  describe 
here)  it  is  shown  (i)  that  gravity  is  an  uniformly  acceler- 
ating force,  that  is,   that  the  increments  of  velocity  in 
equal  times  are  equal  3(2)  that  the  rate  of  increase  varies 


204 


INDUCTIVE  METHODS, 


slightly  at  different  places  on  the  earth's  surface  ;  (3)  that, 
in  the  latitude  of  Greenwich,  in  vacuo,  and  at  high-water 
mark,  the  rate  of  acceleration  for  every  second  of  time 
is  32*19  inches,  the  space  traversed  in  the  first  second 
of  time,  if  the  body  fall  from  rest,  being  half  that  quan- 
tity, so  that  the  spaces  traversed  in  successive  units  of 
time  vary  as  the  odd  numbers  i,  3,  5  .  .  .  .  {211—  i). 
A  slight  degree  of  attention  will  show  that  it  is  by  the 
Method  of  Concomitant  Variations  that  all  these  con- 
clusions are  obtained  ■'^'. 

The  conclusions  based  on  statistics  in  moral  and 
social  enquiries  are  also  instances  of  this  application  of 
the  Method  of  Concomitant  Variations.  It  is  argued 
that,  if  the  same  causes  continue  to  operate  with  like 
intensity  and  no  new  causes  intervene,  the  numerical 
relations  established  between  two  classes  of  social  phe- 
nomena, as,  for  instance,  deficient  education  and  crime, 
may  be  expected  to  remain  constant. 

A  very  important  application  of  the  Method  of  Con- 
comitant Variations  is  what  is  now  commonly  known 
as  the  Historical  Method.  The  Method  designated  by 
this  name  is,  in  fact,  simply  the  Method  of  Concomitant 
Variations  applied  to  facts  furnished  by  history  or  to 
a  record  of  observations  on  the  same  classes  of  facts  as 
those  with  which  history  deals.  It  is  specially  applicable 
to  those  sciences  which  deal  with  man  as  a  progressive 

''  The  student  who  wishes  for  more  detailed  information  on  this 
subject  is  referred  to  Professor  Price's  Iiifmitesimal  Calculus,  vol.  iii. 
chap.  viii.  sect.  3. 


METHOD   OF  CONCOMITANT  VARIATIONS.      205 

being,  or,  at  least,  a  being  capable  of  progress.  Thus, 
a  certain  institution,  custom,  or  opinion  is  traced  through- 
out various  stages  of  society,  and  its  growth  or  decline 
is  connected  with  that  of  some  other  institution,  custom, 
or  opinion,  or  with  the  general  state  of  civilisation  pre- 
valent throughout  these  periods,  it  being  argued,  in  the 
latter  case,  that,  as  civilisation  advances,  the  institution, 
custom,  or  opinion  has  grown  or  declined,  as  the  case 
may  be.  This  method  has  of  late  years  been  employed 
with  great  success  in  the  domains  of  law,  morals,  religion, 
art,  and  language "  ;  and  it  is  sufficient  to  refer  the 
student  for  examples  to  works  such  as  those  of  Sir 
Henry  Maine,  Sir  John  Lubbock,  Professor  Max  Miiller, 
and  Dr.  Tylor.  The  gradual  process  by  which  the  or- 
ganisation of  the  family  passes  into  that  of  the  state, 
or  by  which  the  primitive  feeling  of  resentment  is  de- 
veloped into  that  strict  sense  of  justice  which  distin- 
guishes civilised  man,  would  be  amongst  the  many  striking 
illustrations  of  this  method  which  are  afforded  by  writers 
on  morals  and  society,  both  ancient  and  modern.  When 
the  method  is  combined  with  deductions  from  the  science 
of  Psychology  stating  a  priori  what  might  be  expected 
from  a  general  knowledge  of  human  nature,  it  is  called 
by  Mr.  Mill  the  Ifiverse  Deductive  Method.  Under  this 
head  I  shall  briefly  advert  to  it  again,  in  the  chapter  on 
the  Relation  of  Induction  to  Deduction  ^*. 

"  The  instances  given  on  pp.  200-202  are  examples  of  the  appli- 
cation of  the  Historical  Method  to  the  Science  of  Language. 

*'  There  is  one  objection  to  the  employment  of  the  Historical 
Method,  which  at  least  demands  an  answer.     The  progress,  say,  of 


2o6 


INDUCTIVE  METHODS. 


The  Method  of  Concomitant  Variations,  especially 
when  applied  to  subjects  other  than  physical,  such  as 
law,  morals,  language,  social  statistics,  &c.,  is  often  called 
vaguely  the  Comparative  Method, 

morality,  art,  or  some  particular  institution,  is  compared  with  the 
progress  of  general  civilisation.  But  perhaps  this  very  circumstance 
is  amongst  the  most  important  considerations  to  be  taken  into 
account  in  estimating  the  stage  of  civilisation  to  which  any  people 
or  class  has  attained.  The  scientific  enquirer,  therefore,  who 
employs  the  Historical  Method  seems  to  be  open  to  the  objection 
that  he  is  making  one  quality  vary  as  an  aggregate  of  qualities  of 
which  it  is  itself  one  ;  for,  supposing  the  extreme  case  of  the  other 
ijualities  which  make  up  the  aggregate  being  all  constant,  we  should 
then  have  the  identical  proposition  that  the  quality  or  institution  in 
(juestion  varies  as  itself.  But,  as  a  matter  of  fact,  we  know  that  the 
other  qualities  which  make  up  the  aggregate  of  circumstances  which 
we  call  civilisation  are  far  from  being  constant.  Moreover,  they  are  all 
so  intertwined  with  one  another  that  almost  any  one  of  them  varie» 
<lirectly  as  almost  any  other.  Amongst  these  various  circumstances, 
however,  we  are  able  to  detect  one  on  which  all  the  others  seem  to 
be  specially  dependent.  This  is,  to  state  it  in  the  most  general 
terms,  the  intellectual  condition  prevalent  at  the  given  time,  in  the 
given  place,  or  amongst  the  given  class.  Not  only  do  we  find,  as  a 
matter  of  fact,  that  the  current  intellectual  beliefs  and  the  degree  of 
development  of  the  intellectual  faculties  is  the  best  index  to  the  state 
of  the  other  constituents  which  make  up  civilisation,  but  also  we 
should  expect  a  priori  that  these  latter  circumstances  would  be 
mainly  determined  by  the  former.  For  it  is  by  the  exercise  of 
reason  that  man  learns,  in  an  infinite  variety  of  ways,  to  adapt  him- 
self to  the  various  circumstances  which  surround  him,  that  he 
discovers  the  means  of  gratifying  his  higher  tastes,  and  that  he  is 
enabled  to  enter  into  the  feelings  and  understand  the  wants  of  others. 
On  this  relation  between  the  state  of  the  intellectual  faculties  and 
the  aggregate  of  circumstances  which  constitute  civilisation,  the 
student  may  consult  Mr.  Mill's  logic,  Bk.  VI.  ch.  x.  §  7. 

The  term  '  Historical/  as  designating  this  Method,  is  somewhat 


SUMMARY  OF  RESULTS. 


207 


Briefly  to  review  these  Methods,  it  will  be  seen  that 
we  can  only  arrive  at  absolute  certainty  by  means  of 
one  or  other  of  the  Methods  of  Difference,  Residues,  or 
Concomitant  Variations,  while  the  Method  of  Agreement 
and  the  Joint  Method  of  Agreement  and  Difference  give 
conclusions  only  of  more  or  less  probability,  a  probability, 
however,  which  sometimes  amounts  to  moral  certainty. 
The  Joint  Method  of  Agreement  and  Difference,  or  the 
Double  Method  of  Agreement,  possesses  one  advantage 
over  all  the  other  Methods,  namely  that,  supposing  it  to 
have  been  satisfactorily  ascertained  by  this  Method  that  A 
is  the  cause  of  o,  it  will  follow  that  it  is  the  only  cause. 

It  should  also  be  borne  in  mind  that  a  wide  distinc- 
tion exists  between  those  cases  in  which  the  induction 
indicates  the  precise  character  of  the  causal  connexion 
which  subsists  between  two  or  more  phenomena  and 
those  in  which  it  simply  points  out  that  there  exists  a 
causal  connexion  of  some  kind  or  other.  In  the  latter 
case  a  new  induction  is  required  in  order  to  show  what 
the  nature  of  the  causal  connexion  is. 

It  may  be  noticed,  finally,  that  the  Inductive  Methods 
are  strictly  reducible  to  two  only,  the  Method  of  Agree- 
ment and  the  Method  of  Difference;  the  Joint  Method  of 
Agreement  and  Difference  being  a  double  employment  of 
the  Method  of  Agreement,  supplemented  by  an  employ- 
misleading,  because,  though  the  facts  to  which  the  Method  is  ap- 
plied may  be  mainly  supplied  by  history,  they  are  also,  to  a  large 
extent,  taken  from  the  contemporary  observation  of  tribes  and  peoples 
living  in  different  stages,  or  different  phases,  of  civilisation  with 
reference  to  the  matters  of  enquiry. 


208 


INDUCTIVE  METHODS. 


ment  of  the  Method  of  Difference,  the  Method  of  Con- 
comitant Variations  being  a  series  of  employments  of  the 
Method  of  Difference,  and  the  Method  of  Residues, 
though  employed  in  an  inductive  enquiry,  being  rather  of 
the  nature  of  a  deductive  than  an  inductive  method. 


Note  I. — In  the  preceding  chapter  no  allusion,  or  only 
a  casual  one,  has  been  made  to  a  circumstance  which 
frequently  occasions  an  insuperable  difficulty  in  the  appli- 
cation of  the  Inductive  Methods,  namely,  the  Intermixture 
of  Effects.  It  has  been  supposed  that  the  antecedents 
A,  B,  C,  D,  &c.  are  followed  by  the  consequents  0,3,7,^,*, 
c\:c.,  the  effects  being  regarded  as  heterogeneous  and  not 
homogeneous.  But,  suppose  the  effect  of  A  to  be  a,  of  B  to 


be 


a 


,  of  C  to  be  y,  of  D  to  be  -,  and  of  E  to  be  —  '^j  the 
23  2 


total  effect  of  A,  B,  C,  D,  E  will  be  -  +  ^.    It  is  obvious 

20 

how  difficult  it  would  be  in  this  case  to  discover  either 
the  exact  portion  of  the  effect  which  is  due  to  each  cause 
or  the  several  causes  which  operate  to  produce  the  total 
effect.  We  might  have,  in  fact,  as  in  mechanical  action 
and  reaction,  A  producing  a  and  B  producing  —  a,  each 
cause  thus  neutralising  the  effect  of  the  other,  so  that 
we  might  entertain  no  suspicion  that  the  causes  A  and  B 
were  in  operation  at  all.  In  these  cases,  our  main  re- 
source is  Deduction.  Having  ascertained  separately  by 
one  or  other  of  the  various  inductive  methods,  or  from 
previous  deductions,  the  effects,  say  of  A,  B,  C,  D,  we 


INTERMIXTURE   OF  EFFECTS, 


209 


calculate  deductively  their  combined  effect,  and  then,  by 
subtracting,  according  to  the  Method  of  Residues,  the 
sum  of  the  known  causes  from  the  total  aggregate  of 
causes  and  the  known  portion  of  the  effect  from  the 
total  effect,  we  simplify,  if  we  do  not  solve,  the  problem. 
On  the  insufficiency,  under  ordinary  circumstances,  of 
the  Inductive  Methods,  without  the  aid  of  Deduction,  to 
grapple  with  cases  of  this  kind  ""■',  and  on  the  nature  of 
the  assistance  rendered  by  Deduction,  the  reader  may  con- 
sult Mr.  Mill's  Logic,  Bk.  III.  ch.  x.  §  4-8,  and  ch.  xi. 

In  cases  of  this  kind,  where  the  action  of  one  cause 
is  augmented,  diminished,  or  wholly  counteracted  by  that 
of  another,  it  must  not  be  supposed  that  any  part  of  its 
appropriate  effect  has  failed  to  be  produced,  even  though 
it  may  have  disappeared  wholly  or  partially  in  the  total 

'^  Since  the  appearance  of  the  first  edition  of  this  work,  it  has 
been  pointed  out  by  Mr.  Bain  that  '  Concomitant  Variation  is  the 
only  one  of  the  [Inductive]  Methods  that  can  operate  to  advantage 
in  such  cases.'  I  take  the  liberty  of  transcribing  the  passage  :  *  If 
a  cause  happens  to  vary  alone,  the  effect  will  also  vary  alone,  and 
cause  and  effect  may  be  thus  singled  out  under  the  greatest  compli- 
cations. Thus,  when  the  appetite  for  food  increases  with  the  cold, 
we  have  a  strong  evidence  of  connexion  between  those  two  facts, 
although  other  circumstances  may  operate  in  the  same  direction. 

•  The  assigning  of  the  respective  parts  of  the  sun  and  moon,  in 
the  action  of  the  Tides,  may  be  effected,  to  a  certain  degree  of 
exactness,  by  the  variation  of  the  amount  according  to  the  positions 
of  the  two  attracting  bodies. 

*By  a  series  of  experiments  of  Concomitant  Variations,  directed 
to  ascertain  the  elimination  of  nitrogen  in  the  human  body  under 
varieties  of  muscular  exercise,  Dr.  Parkes  obtained  the  remarkable 
conclusion,  that  a  muscle  grows  during  exercise  and  loses  bulk  during 
the  subsequent  rest.'— Bain's  Logic,  Bk.  III.  ch.  viii.  §  6. 


210 


INDUCTIVE  METHODS, 


result.  An  object  may  remain  at  rest,  when  subject 
to  two  equal  forces  acting  in  opposite  directions,  but 
we  cannot  say  of  either  of  these  forces  that  it  is  in- 
operative :  each,  it  is  true,  prevents  any  visible  effect 
resulting  from  the  other ;  but  then  this  is  the  very  effect 
which  it  produces,  and  the  correct  mode  of  describing 
either  of  the  opposing  forces  would  be  to  say  that 
it  has  a  tendency  to  make  the  given  object  move  with 
a  certain  velocity  in  a  certain  direction.  The  student 
cannot  too  constantly  bear  in  mind  that  every  cause 
invariably  produces  its  full  effect,  though  other  causes 
may  prevent  that  effect  from  manifesting  itself  with  all 
the  intensity  with  which  it  would  manifest  itself,  if  it  acted 
alone ;  that  there  are,  strictly  speaking,  no  exceptions  to 
laws  of  nature,  though  these  laws,  in  their  manifold  action 
and  reaction,  may  modify  or  even  neutralise  each  other. 
The  aphorism  '  Every  rule  has  an  exception,'  is  only  true, 
even  in  Grammar,  either  because  the  rule  is  inexactly 
stated  or  because  it  conflicts  with  some  other  rule  known 
or  unknown. 

Note  2. — The  Canons  for  the  Inductive  Methods  were 
first  stated  by  Mr.  Mill,  and  the  importance  now  attached 
to  them  in  most  analyses  of  inductive  enquiries  is  mainly 
due  to  his  influence.  The  methods  are,  however,  as 
Mr.  Mill  himself  states,  'distinctly  recognised'  in  Sir 
John  Herschel's  Discourse  on  the  Study  of  A\itural  Phi- 
losophy^ so  often  quoted  in  this  work,  'though  not  so 
clearly  characterised  and  defined,  nor  their  correlation 
so  fully  shown,  as  has  appeared  to  me  desirable.'     In 


ANTICIPATED  BY  BACON 


211 


the  Second  Book  of  Bacon's  Novum  Organum,  we  find 
some  approximations,  very  rough,  it  is  true,  to  formal 
inductive  methods.  The  '  instantiae  crucis '  have  already 
been  adduced  as  examples  of  the  Method  of  Difference, 
and  the  '  instantiae  solitarioe '  as  comprising  examples 
of  both  the  Method  of  Agreement  and  the  Method  of 
Difference ;  but  the  part  of  the  Novum  Organiwi  to 
which  I  am  now  alluding,  and  which  is  intended  to  be 
of  more  universal  application  than  the  '  instantiae  crucis  ' 
and  the  *  instantiae  solitariae,'  is  contained  in  the  early 
Aphorisms  of  the  Second  Book.  Certain  Tables  of 
Instances  are  there  given  for  the  purpose  of  providing 
materials  with  which  to  conduct  an  investigation  into 
what  Bacon  called  the  '  Form  •''^,'  corresponding  pretty 
nearly,  at  least  in  this  connexion,  with  what  we  should 
call  the  '  Cause,'  of  Heat.  The  instances  are  very  far 
from  satisfying  the  conditions  of  Mr.  Mill's  Methods,  but 
the  principles  on  which  they  are  arranged  in  Tables 
bear  a  close  analogy  to  the  principles  on  which  the 
Canons  are  constructed.  The  best  mode,  perhaps,  of 
enabling  the  student  to  perceive  the  extent  of  the  resem- 
blance is  to  state  the  conditions  with  which  the  instances 
in  Bacon's  Tables  would  be  required  to  conform,  in  order 
to  satisfy  the  requirements  of  Mr.  Mill's  Methods. 

If  the  '  Instantiae  convenientes  in  natura  calidi '  "^  were 


^  On  the  meaning  attached  by  Bacon  to  the  word  *  Form,*  and 
its  relation  to  *  Essence '  and  *  Cause,'  see  the  Introduction  to  my 
Edition  of  the  Novum  Organum,  §  8. 

^  Novum  Organuin,  Lib.  II.  Aph.  xi. 

P   2 


212 


INDUCTIVE  METHODS. 


SO  related  to  one  another  that,  besides  the  given  pheno- 
menon (heat),  only  one  other  circumstance  were  common 
to  them  all,  that  other  circumstance  might  be  regarded, 
with  more  or  less  probability,  as  the  cause  (or  effect)  of 
heat,  or,  at  least,  as  connected  with  it  through  some  fact 
of  causation.  Such  instances  would  then  come  under 
the  Method  of  Agreement. 

If  one  instance  in  the  Table  of  Agreement  (*  Instantiae 
convenientes  in  natura  calidi  ')  were  so  related  to  one 
of  the  instances  in  the  Table  of  Privation  ('  Instantiae  in 
proximo,  quae  privantur  natura  calidi ')  ^^  as  to  have  every 
circumstance  in  common  with  it,  except  that  the  former, 
besides  presenting  the  phenomenon  of  heat  which  is 
supposed  to  be  absent  in  the  latter,  also  presented  some 
other  circumstance  which  was  absent  from  the  latter,  this 
other  circumstance  would  be  the  cause  (or  effect),  or  a 
necessary  part  of  the  cause,  of  heat.  We  should  here 
have  the  Method  of  Difference. 

If,  in  the  '  Tabula  graduum,  sive  comparativae  in 
calido  *'^'  we  could  discover  some  one  phenomenon  which 
increased  and  diminished  proportionately  with  the  increase 
and  diminution  of  heat,  that  phenomenon  would  be  the 
cause  or  the  effect  of  heat,  or,  at  least,  connected  with  it 
through  some  fact  of  causation,  and  the  conditions  would 
thus  conform  with  the  requirements  of  the  Method  of 
Concomitant  Variations.  If  it  could  be  shown  that  this 
phenomenon  and  heat  were  the  only  circumstances 
which  varied  concurrently,  then  the  phenomenon  would 

^'  Novum  Organum,  Lib.  II.  Aph.  xxii.  ^  Id.  Aph.  xiii. 


ANTICIPATED  BY  BACON, 


213 


be  proved  to  be  either  the  cause  or  the  effect  of  heat, 
and  would  conform  with  the  requirements  of  the  rider  to 
this  last  Method  (p.  186). 

The  *  Exemplum  exclusivae,  sive  rejectionis  naturarum 
a  forma  calidi '  ®'  (which  is  based  on  the  foregoing  Tables) 
bears  some,  though,  it  must  be  acknowledged,  a  very 
slight,  resemblance  to  the  Method  of  Residues.  These 
*  rejectiones  '  consist  in  excluding  some  possible  explana- 
tion of  the  phenomenon,  either  because  an  instance, 
which  does  not  present  the  phenomenon,  does  present 
the  assigned  cause,  or  because  an  instance,  which  does 
present  the  phenomenon,  does  not  present  the  assigned 
cause  ^^  (and  similarly  with  regard  to  increase  and  de- 
crease). As  an  example  of  the  former  case,  we  may 
take  the  following  '  rejectio  ' :  *  Per  radios  lunae  (which 
were  then  supposed  to  be  cold)  et  aliarum  stellarum  rejice 
lucem  et  lumen.'  As  examples  of  the  latter,  we  may  take 
the  two  following :  *  Per  radios  solis,  rejice  naturam  ele- 
mentarem  (that  is,  *  terrestrial  nature,'  which  is  composed 
of  *  the  four  elements ') ;  Per  ignem  communem,  et 
maxime  per  ignes  subterraneos  (qui  remotissimi  sunt,  et 
plurimum  intercluduntur  a  radiis  coelestibus)  rejice  na- 
turam coelestem.'  By  a  succession  of  these  '  rejectiones,' 
we  limit  the  number  of  possible  explanations,  amongst 
which  we  are  to  look  for  the  true  one.     Bacon's  '  rejec- 


*'  Novum  Organum,  Lib.  II.  Aph.  xviii. 

"2  The  latter,  of  course,  is  not  a  legitimate  argument.  The  effect 
may  be  due  to  several  distinct  causes,  a  fact  which  was  not  recognised 
by  Bacon.     See  my  notes  on  Novum  Organum,  Lib.  II.  Aph.  xvi. 


214 


INDUCTIVE  METHOD 


tions,'  however,  not  being,  as  a  matter  of  fact,  exhaustive, 
lead  to  a  purely  negative  result ;  they  may  save  us  from 
unnecessary  trouble  in  seeking  for  a  cause  where  it 
cannot  be  found,  but  they  do  not,  like  the  Method  of 
Residues,  leave  a  definite  number  of  antecedents  which 
either  constitute  the  cause,  or  amongst  which  we  know 
that  the  cause  is  to  be  sought. 

It  is  plain  that  if  there  were  a  certain  number  only  of 
possible  causes  of  the  given  phenomenon,  and  by  the 
method  of  rejections  we  could  exclude  all  but  one,  this 
one  remaining  cause  would  be  the  undoubted  cause  of 
the  given  phenomenon.  This  case  Bacon  appears  to 
have  regarded  as  the  perfect  type  of  Induction,  and  as 
alone  capable  of  affording  certainty  ^''. 

Note  3. — Dr.  Whewell  (in  a  pamphlet  published  in 
1849,  which  is  now  embodied  in  the  Philosophy  of  Dis- 
covery^^') questions   the   utility  of  the    Four  Methods. 

•'  It  must  be  understood  that,  in  this  note,  I  am  simply  comparing 
the  'Tables'  of  Bacon  with  the  *  Methods'  of  Mr.  Mill.  On  the 
relation  of  the  *  Tables  '  to  each  other  and  on  the  special  importance 
attached  by  Bacon  to  the  'Rejections,'  the  student  may  consult 
§  9  of  the  Introduction  to  my  edition  of  the  A^oviim  Organum 
(Clarendon  Press)  and  my  notes  to  the  earlier  aphorisms  of  the 
Second  Book. 

In  comparing  the  logical  procedure  of  Bacon  and  Mill,  it  should 
be  carefully  borne  in  mind  that  Bacon  contemplated  the  concurrent 
use  of  all  the  Tables,  as  preparatory  to  his  Method  of  Rejections, 
and  regarded  the  construction  of  the  Tables  and  the  subsequent  ap- 
plication to  them  of  the  Method  of  Rejections  as  constituting  only 
one  process.  On  the  other  hand,  each  of  Mr.  Mill's  Methods  may 
be  worked  independently,  and  lead  to  a  final  conclusion. 

•*  See  Philosophy  of  Discovery^  ch.  xxii.     The  criticism  of  Mr. 


CRITICISMS  OF  THEM. 


2^15 


*  Upon  these  methods,'  he  says,  '  the  obvious  thing  to 
remark  is,  that  they  take  for  granted  the  very  thing  which 
is  most  difficult  to  discover,  the  reduction  of  the  pheno- 
mena to  formulae  such  as  are  here  presented  to  us.'  He 
also  objects  that,  as  a  matter  of  fact,  no  discoveries  have 
ever  been  made  by  the  employment  of  these  methods. 
*Who  will  carry  these  formulae  through  the  history  of 
the  sciences,  as  they  have  really  grown  up,  and  show  us 
that  these  four  methods  have  been  operative  in  their 
formation  ;  or  that  any  light  is  thrown  upon  the  steps  of 
their  progress  by  reference  to  these  formulae  ? ' 

The  first  objection  is,  as  Mr.  Mill  points  out,  of  the 
same  character  with  the  objections  raised  by  Locke  and 
other  writers  of  the  eighteenth  century  against  the  Rules 
of  Syllogistic  Reasoning.  The  reply,  in  either  case,  is 
that  Logic  does  not  profess  to  supply  arguments,  but  to 
test  them.  Men  have  certainly  reasoned,  and  reasoned 
with  the  greatest  success,  without  any  conscious  use  of 
the  rules  of  Logic.  But  it  is  the  province  of  a  system  of 
Logic  to  analyse  the  arguments  commonly  employed,  to 
discriminate  between  those  which  are  correct  and  those 
which  are  incorrect,  and  thus  to  enable  men  to  detect, 
in  the  case  of  others,  and  to  avoid,  in  their  own  case, 
erroneous  methods  of  reasoning.  To  think  of  appro- 
priate arguments  is  undoubtedly  more  difficult  than  to 
test  them  ;  but  this  fact  does  not  obviate  the  necessity  of 
submitting  them  to  a  test.     Nor  is  it  a  more  real  objec- 

Mill's  Methods  will  be  found  in  §§  38-48.     Mr.  Mill  replies  in  a 
note  at  the  end  of  Bk.  III.  ch.  ix. 


2l6 


INDUCTIVE   METHODS, 


tion  that  men,  who  know  nothing  of  the  technical  rules 
of  Logic,  often  reason  faultlessly  themselves,  and  show 
remarkable  acuteness  in  detecting  inconclusive  reasoning 
in  the  arguments  of  others.  Many  men  speak  gram- 
matically without  having  learnt  any  system  of  grammar ; 
in  the  same  manner,  many  men  reason  logically  with- 
out having  learnt  any  system  of  Logic.  But  the  great 
majority  of  men,  there  can  be  little  doubt,  may  derive 
assistance  both  from  one  and  the  other.  Grammar 
fulfils  its  functions  when  it  raises  the  student  to  the  level 
of  the  most  correct  speakers ;  similarly.  Logic  fulfils  its 
functions  when  it  raises  the  student  to  the  level  of  the 
best  reasoners.  As  applied  to  the  syllogistic  rules  and 
formulae,  this  defence  would  now  be  generally  admitted, 
but  it  holds  equally  good  of  the  methods  under  which 
it  may  be  shown  that  our  inductive  arguments  may  ulti- 
mately be  arranged.  '  The  business  of  Inductive  Logic,' 
says  Mr.  Mill,  '  is  to  provide  rules  and  models  (such  as 
the  Syllogism  and  its  rules  are  for  ratiocination)  to  which 
if  inductive  arguments  conform,  those  arguments  are 
conclusive,  and  not  otherwise.  This  is  what  the  Four 
Methods  profess  to  be,  and  what  I  believe  they  are 
universally  considered  to  be  by  experimental  philoso- 
phers, who  had  practised  all  of  them  long  before  any 
one  sought  to  reduce  the  practice  to  theory.' 

With  regard  to  the  second  objection,  that  these  me- 
thods have  not  been  operative  in  the  formation  of  the 
sciences,  Dr.  Whewell  seems  to  ignore  the  distinction 
between  the  conscious  and  the  unconscious  employment 


CRITICISMS  OF  THEM, 


217 


of  a  method.     It  is  undoubtedly  true  that  in  records  of 
scientific  investigations  we  seldom  find  the  formal  lan- 
guage in  which  the  Inductive  Canons  are  expressed.     It 
seems  to  me  equally  true  that  in  such  records  we  inva- 
riably detect  the  employment  of  the  Canons  themselves. 
Discoveries  are  of  two  kinds  :  they  are  either  entirely  the 
result  of  patient  research,  or  they  are  first  suggested  to 
the    mind    by    some    brilliant   thought,    and   afterwards 
verified    by  rigorous   proof.     In    the   former   case,  the 
discoverer  must   have  made  sure  of  his   ground  as  he 
proceeded,  and,  so  far  as  his  method  was  inductive,  he 
could   only  do  so  by  appealing,  consciously  or  uncon- 
sciously, to  one  or  more  of  the  inductive  methods  ;  if  he 
acted   otherwise,  he   arrived  at  a  true    result   by    mere 
accident.     In  discussing  the  latter  case,  I  must  repeat 
what  has  already  been  stated,  that  it  is  not  the  ofifice  of 
Logic,  either  inductive  or  deductive,  to  suggest  thoughts, 
but  to  analyse  and  to  test  them.     Now,  in  the  case  we 
are  supposing,  the  discovery  really  consists  of  two  parts 
— the   original  conception  and    the  subsequent  process 
by  which  it  is  determined  to  be  the   true   explanation 
of  the  phenomenon.     However  striking  and  appropriate 
the  conception,  we  have  no  right  to   regard   it  as  the 
true   explanation  of  the   phenomenon  till   it  has   been 
subjected  to  the  most  rigorous  investigation.     This  in- 
vestigation   must   be  either  inductive   or   deductive,  or 
both.     But,  so  far  as  it  is  inductive,  it  must  conform 
with  the  requirements  of  the  Inductive  Canons,  or  else  it 
will  not  result   in  positive   proof,  or  even  approximate 


ai8 


INDUCTIVE  METHODS, 


closely  to  it.  As  in  the  former  case,  unless  the  dis- 
coverer has,  consciously  or  unconsciously,  reasoned  in 
strict  conformity  with  the  requirements  of  Logic,  he  has 
no  right  to  feel  any  confidence  in  the  result  of  his 
researches. 

It  may  be  added  that  appropriate  conceptions,  pro- 
mising to  be  fertile  in  scientific  results,  are  only  likely, 
as  a  rule,  to  occur  to  persons  whose  minds  have  been 
habitually  disciplined  by  the  strict  observance,  conscious 
or  unconscious,  of  the  laws  of  reasoning.  Originality  is 
not  a  quality,  as  some  seem  to  think,  which  admits  of  no 
psychological  explanation. 

I  have  not  thought  it  desirable  to  discuss  more  recent 
criticisms  of  the  Inductive  Methods,  because,  apart  from 
the  stress  which  they  lay  on  the  difficulty  of  satisfying 
the  conditions  of  the  Canons  (a  difficulty  which  is  ac- 
knowledged on  all  sides  to  exist,  at  least  in  many  cases), 
I  cannot  think  that  they  have  added  materially  to  the 
objections  raised  by  Dr.  Whewell. 

• .  •  The  student  is  particularly  requested  to  read,  in 
connexion  with  this  chapter,  the  *  Preface  to  the  Third 
Edition,'  reprinted  at  the  beginning  of  the  Book.  This 
Preface  deals  with  certain  controverted  points  respecting 
the  certainty  of  Inductive  Reasoning  and  the  nature  of 
the  assumptions  made  in  it,  with  which,  though  they 
could  not  conveniently  be  introduced  into  the  body  of 
the  book,  it  is  desirable  that  the  student  should  acquaint 
himself. 


CHAPTER    IV. 


Of  Imperfect  Inductions. 


AN  argument  from  the  particular  to  the  general,  or 
from  particulars  to  adjacent  particulars,  may  fall  short  of 
absolute  proof,  or  even  of  moral  certainty,  while  it  com- 
mends itself  as  possessing  more  or  less  of  probability. 
Arguments  of  this  character  may  be  called  Imperfect 
Inductions.  Under  this  head  fall  imperfect  applications 
of  the  experimental  or  inductive  methods,  the  argument 
from  analogy,  and  incomplete  cases  of  Inductio  per  enu- 
merationem  si??ip/icem. 

The  Inductio  per  e mi meratione^n  simplicem  is,  as  alread\- 
noticed  ',  when  complete  {Ifiductio  Coinpleta\  a  deductive, 
and  not  an  inductive,  argument.  When  mcomplete,  it  is 
an  inductive  argument,  for  it  is  an  inference  of  the  general 
from  the  particular  or  the  unknown  from  the  known. 
This  form  of  Induction  affords  certainty  only  when,  as  in 
the  case  of  the  Laws  of  Universal  Causation  and  of  the 
Uniformity  of  Nature,  or  of  the  Mathematical  Axioms, 

'  See  p.  125,  note  2,  and  Deductive  Logic,  Part  III.  chap.  i.  ap- 
pended note  2. 


220 


IMPERFECT  INDUCTIONS, 


it  is  grounded  upon  universal  experience,  and  we  feel 
assured  that,  if  there  had  been  at  any  time  or  were  now 
in  any  place  any  instance  to  the  contrary,  it  would  not 
have  escaped  our  notice.     But,  in  ordinary  cases,  the 
incomplete  Inductio  per  enumerationem  shnplicetn  affords 
only  a  presumption,    sometimes  very  slight,  sometimes 
tolerably    strong,  in  favour  of  the  position  which  it  is 
adduced  to  establish.     I  perceive,  say  in  five,  ten,  or 
twenty  cases,  that  the  phenomenon  a  is  attended  by  the 
phenomenon  b^  and,  knowing  of  no  cases  in  which  the 
one  phenomenon  is  not  attended  by  the  other,  I  begin 
to  suspect  that  a  and  b  are  connected  together  in  the 
way  of  causation.     Such  a  surmise  may  afterwards  be 
proved  by  the  aid  of  one  or  other  of  the  five  methods 
to  be  correct,  and,  in  that  case,  it  is  taken  out  of  the 
categor)'  of  inductions  per  enumerationem  simplicem^  and 
becomes  an  instance  of  a  scientific  induction.     But,  if 
neither  proved  nor  disproved,  it  still  has  a  certain  amount 
of  probability  in  its  favour,  that  amount  depending  on 
the  two   following  considerations:    (i)  the   number   of 
positive    instances  which  have  occurred  to  us;  (2)  the 
likelihood,  if  there   be  any  negative  instances,    of  our 
having  met  with  them.     The  first  of  these  considerations 
deserves  little  weight,  unless  supported  by  the  other.     A 
native  of  the    North  of  Europe,    some   centuries   ago, 
might,   if  the  mere  accumulation  of  positive  instances 
were  sufficient,  have  taken  it  for  a  certain  truth  that  all 
men  had  white  complexions.     His  own  personal  observa- 
tion, as  well  as  the  reports  of  travellers  and  the  traditions 


INDUCTIO  PER   ENUM.   SIMP. 


221 


of  his  race,  would  have  furnished  numberless  instances 
in  favour  of  the  position.     But,  before  drawing  the  in- 
ference, he  ought  to  have  reflected  that  he  possessed 
information  about  a  small  portion  only  of  the  inhabitants 
of  the  earth's  surface,  that  a  difference  of  climate  might 
produce  a  difference  of  complexion,  and  that  there  was 
no  reason  for  supposing  that  the  anatomical  structure  of 
man,  or  the  various  characteristics  which  we  denominate 
human,  are  necessarily  connected   with   a  skin  of  one 
particular  colour.     But,  on  the  other  hand,  we  may  affirm 
with  tolerable  certainty  that  all  the  varieties  of  beings 
possessing  the  physical  structure  of  man  have  the   ca 
pacity  of  articulate  speech  ;  for,  if  there  were  any  races 
exhibiting  the  one  set  of  phenomena  without  the  other, 
there  is  every  probability,  with  our  present  knowledge  of 
the  earth's  surface,  that  we  should  be  acquainted  with 
their  existence.     In  this  instance  the  first  consideration, 
which  in  itself  would  deserve  little  weight,  is  converted 
into  a  certainty  almost  absolute  by  the  support  which  it 
derives  from  the  second. 

It  cannot  be  too  strongly  impressed  on  the  mind  of 
the  student  that  a  mere  enumeratio  simplex^  that  is, 
a  mere  assemblage  of  positive  instances,  unless  we  have 
reason  to  suppose  that,  were  there  any  instances  to  the 
contrary,  they  would  have  become  known  to  us,  is  simply 
worthless.  *  Inductio  quie  procedit  per  enumerationem 
sijnplicem  res  puerilis  est.'  But  if  the  enumeratio  simplex 
be  accompanied  by  a  well-grounded  conviction  that  there 
are  no  instances  to  the  contrary,  it  may  afford  a  very 


222 


IMPERFECT  INDUCTIONS, 


high  degree  of  probability,  and,  if  we  can  assure  our- 
selves that  there  are  no  instances  to  the  contrary,  to  us 
individually  it  will  afford  certainty. 

It  might  seem  that  an  Inductio  per  Enumerationem 
Simplicem  is  always  an  employment  of  the  Method  of 
Agreement.  But  there  is  this  essential  difference.  The 
Method  of  Agreement  is  a  method  of  elimination,  select- 
ing some  and  rejecting  other  instances,  and  founding  its 
conclusion  not  on  the  quantity  but  on  the  character  of 
the  instances  which  it  selects.  The  Inductio  per  Enu- 
merationem Simplicem,  on  the  other  hand,  depends  for 
its  validity  on  the  number  of  instances  ;  the  instances, 
indeed,  must  be  gathered  from  every  available  field,  and 
hence  sometimes  we  speak  of  their  variety  as  well  as 
their  quantity,  but  the  one  essential  characteristic  of 
the  method  is  that  it  does  not  select,  but  accumulate 
instances.  A  few  well-selected  instances  are  often  suffi- 
cient to  satisfy  the  requirements  of  the  Method  of 
Agreement.  The  same  number,  when  we  abstract  the 
grounds  on  which  they  were  selected,  would  be  utterly 
insufficient  to  justify  an  Inductio  per  Enumerationem 
Simplicem. 

It  may  in  fact  be  remarked  of  all  the  Experimental 
Methods  that  they  are  devices  for  saving  labour.  The 
range  of  our  experience  is  often  insufficient  to  justify  an 
argument  founded  on  an  Inductio  per  Enumerationem 
Simplicem,  but  by  means  of  the  Experimental  or  In- 
ductive Methods  we  so  select  our  instances,  as  to  bring 
the  particular  case  which  we  are  investigating  under  the 


INDUCTIO  PER   ENUM.  SIMP, 


223 


general  laws  of  Universal  Causation  and  the  Uniformity 
of  Nature.  The  validity  of  the  induction  in  question  is 
thus  artificially  connected  with  the  validity  of  these  uni- 
versally accepted  inductions,  and  we  are  enabled  to  argue 
from  the  truth  of  the  latter  to  that  of  the  former. 

Uncontradicted  experience,  of  course,  implies  a  great 
variety  of  instances,  and,  from  this  point  of  view,  every 
well-grounded  Inductio  per  Enumerationem  Simplicem 
might  be  represented  as  an  application  of  the  Method 
of  Agreement.  But  to  represent  it  in  this  form  would 
often  weaken  its  force.  For,  while  our  experience  may 
be  so  wide  as  to  justify  us  in  affirming  the  constant 
union  of  two  or  more  circumstances,  the  number  of 
other  common  circumstances,  known  or  suspected,  with 
which  these  are  found  in  invariable  combination,  may 
be  so  large  as  to  render  it  impossible  for  us  to  satisfy 
even  approximately  the  conditions  of  the  Method  of 
Agreement.  Here,  as  elsewhere,  an  argument  often 
admits  of  being  stated  in  two  ways,  and  it  is  the  office 
of  the  logician  to  state  it  in  that  form  in  which  it  carries 
the  largest  amount  of  conviction,  or  rather  offers  the 
most  satisfactory  kind  of  proof. 

It  is,  as  I  have  already  pointed  out  in  the  First 
Chapter  ^  by  means  of  an  Inductio  per  Enumerationem 
Simplicem  that  we  establish  what  have  been  called 
'  Inductions  of  Co-existence.'  This  is  the  case,  when, 
as   the   result   of  a   wide  experience,    two  phenomena 

»  Pp.  7-9. 


224 


IMPERFECT  INDUCTIONS. 


are  found  to  be  invariably  co-existent,  but  we  have  no 
evidence  to  connect  them  as  cause  and  effect,  or  even 
as  effects  of  the  same  cause.  Such  are  the  attributes 
which  are  found  to  be  invariably  united  in  the  same 
Natural  Kinds,  that  is  to  say,  in  the  same  species  of 
plants,  animals,  and  minerals;  such  are  the  two  pro- 
perties of  Inertia  and  Gravity  which  are  found  united 
in  all  matter.  In  all  these  cases,  there  is  probably  some 
causal  connexion,  hitherto  undetected,  between  the  co- 
existing phenomena ;  but  while  we  are  unable  to  apply 
with  any  success  the  more  refined  inductive  methods, 
we  must  content  ourselves  with  regarding  the  uniformity 
as  simply  one  of  co-existence.  If  we  made  any  pro- 
gress towards  the  discovery  of  a  causal  connexion,  the 
uniformity  would  be  transferred  to  another  category, 
and  would  rank  amongst  the  inductions  discussed  in 
the  last  chapter.  Meanwhile,  these  inductions,  de- 
pending simply  on  uncontradicted  experience,  and  being 
at  present  inaccessible  to  the  Methods  of  Elimination, 
must  be  regarded  as  generalisations  awaiting  further 
investigation '. 

The  term   *  Empirical  Generalisation '  or  '  Empirical 

'^  For  a  further  discussion  of  the  Uniformities  of  Co-existence,  the 
reader  is  referred  to  Mr.  Bain's  Logic,  Bk.  III.  ch.  iii.  I  am  disposed 
to  estimate  more  highly  than  Mr.  Bain  the  probability  that  these 
uniformities  might,  if  our  knowledge  were  extended,  be  ultimately 
resolved  into  Uniformities  of  Causation,  and  hence  they  do  not 
appear  to  me  to  require  any  separate  or  detailed  treatment  in  a 
work  on  Logic. 


EMPIRICAL  LAWS. 


225 


Law'  might  be  conveniently  appropriated  to  express 
those  secondary  laws  (as  distinct  from  Ultimate  Laws 
of  Nature*)  which  are  the  result  of  an  Inductio  per 
Enumerationem  Simplicem.  Though  these  expressions 
are  employed  with  great  latitude,  it  is  usually  regarded 
as  characteristic  of  an  Empirical  Law  or  Generalisation 
that  it  can  only  be  received  as  true  within  the  limits  of 
the  data  from  which  it  is  derived,  that  at  another  time, 
at  another  place,  or  under  different  circumstances  from 
those  under  which  the  observations  were  made,  it  might 
be  found  to  break  down^  It  is  true  that,  owing  to  the 
conflict  of  causes,  this  description  applies  to  many  of 
the  conclusions   arrived  at   by  means  of  the  Inductive 

*  Some  of  these  Ultimate  Laws  of  Nature,  such  as  the  Law  of 
Universal  Causation,  the  Law  of  the  Conservation  of  Energy,  the 
invariable  co-existence  of  Inertia  with  Gravity,  &c.,  appear  to  rest 
simply  on  uncontradicted  experience,  that  is  to  say,  on  an  Inductio 
per  Enumerationem  Simplicem,  and  still  it  would  seem  paradoxical 
to  speak  of  them  as  merely  '  Empirical  Laws.'  An  Empirical  Law 
might,  perhaps,  be  defined  as  a  secondary  law,  the  causal  derivation 
of  which  is  not  yet  known  or  even  surmised  with  any  probability,  or 
as  a  subordinate  generalisation  arrived  at  by  an  Inductio  per  Enu- 
merationem Simplicem  ;  definitions  which,  it  will  be  perceived,  are 
really  identical.  I  have,  however,  avoided  any  special  discussion  of 
what  are  called  *  Empirical  Laws,'  both  on  account  of  the  extremely 
indeterminate  use  of  the  expression,  and  because  such  a  discussion  is 
calculated,  in  my  opinion,  needlessly  to  perplex  the  student  by  the 
complicated  questions  to  which  it  leads.  The  advanced  student  can 
refer  to  Mr.  Mill's  Logic,  Bk.  Ill,  ch.  xv.,  and  Bk.  V.  ch.  v.  §  4,  but 
he  will  be  introduced,  I  venture  to  suggest,  to  more  difficulties  than 
he  will  find  solved. 

*  See  Herschel's  Discourse  on  the  Study  of  Natural  Philosophy ^ 
§  187,  and  Mill's  Logic,  Bk.  III.  ch.  xvi.  §  4. 

Q 


226 


IMPERFECT  INDUCTIONS, 


Methods,  but  it  is  peculiarly  applicable  to  the  results 
of  the  Inductio  per  Enumerationem  Simplicem,  and  it 
would  be  extremely  convenient  to  possess  an  expression 
by  which  the  results  of  this  method  might  be  at  once 
distinguished  from  those  of  scientific  induction  on  the 
one  hand,  and  those  of  analogy  (to  be  discussed  pre- 
sently) on  the  other.  Instances  of  Empirical  Laws  in 
this  restricted  sense  are  such  generalisations  as  that 
certain  animals  or  flowers  *  are  of  a  certain  colour,  that 
certain  tribes  of  men  are  less  capable  of  civilisation  than 
others,  and,  perhaps,  that  certain  appearances  of  sky  are 
indicative  of  certain  changes  of  weather.  There  are,  of 
course,  some  cases  in  which  it  is  difficult  to  determine 
whether  a  given  conclusion  has  been  arrived  at  by  the 
Inductio  per  Enumerationem  Simplicem  or  by  an  im- 
perfect application  of  the  Method  of  Agreement,  that  is  to 
say,  whether  it  is  based  on  instances  taken  indifferently, 
or  on  selected  instances. 

Another  form  of  imperfect  induction  is  the  Argument 
from  Analogy  ^.     Here  we  do  not  argue  from  a  number 

•  The  colours  of  flowers,  however,  seem  to  be  in  a  fair  way  of 
being  accounted  for  by  the  peculiarities  of  their  mode  of  fertilisation. 
See  a  most  interesting  work  on  the  Colours  of  Flowers,  by  Mr.  Grant 
Allen,  published  in  Macmillans' A^a/«AV  Series,  1882. 

^  It  will  be  observed  that  the  word  '  Analogy  '  is  here  employed 
in  the  sense  of  *  resemblance.*  In  the  stricter  and  more  ancient 
meaning  of  the  term,  it  signifies  an  equality  of  relations  (iVcJri;? 
K(>-^(x}v).  See  Aristotle's  Ethics,  Bk.  v.  3  (8).  The  reader  will  find 
the  two  significations  of  the  word  '  Analogy '  discriminated  in  the 
Elements  of  Deductive  Logic,  Part  III.  ch.  i.  note  2. 


ANALOGY, 


227 


of  instances,  as  in  the  case  of  Inductio  per  Enumerati- 
onem Simplicem,  but  from  a  number  of  points  of  resem- 
blance. The  argument  is  not,  that,  because  S,  T,  U,  V, 
W,  &:c.  exhibit  the  union  of  m  with  a,  b,  <r,  we  may 
therefore  expect  to  find  ;;/  in  Z,  or  wherever  else  a, 
b,  c  may  occur ;  but  that,  because  X  and  Y  (any  two 
or  more  instances)  agree  in  the  possession  of  certain 
qualities  ^,  b^  c,  we  may  expect  to  find  the  quality  m 
which  is  presented  by  X  exhibited  also  in  Y.  The 
argument  is  based,  notion  the  number  of  instances  in 
which  the  two  sets  of  qualities  are  found  united,  but  on 
the  number  of  qualities  which  are  found  to  be  common 
to  two  or  more  instances :  the  argument  is  not  that 
I  have  so  often  observed  a^  b^  c  in  conjunction  with  m 

Archbishop  Whately  defines  Analogy  as  a  resemblance  of  Rela- 
tions. This  definition,  if  intended  to  represent  the  ancient  signifi- 
cation of  the  word,  is  incorrect.  The  Aristotelian  Analogy  is  an 
equality,  not  a  resemblance  of  relations.  The  instance  given  in  Eth. 
Nic.  i.  6  (12)  is  that,  in  man,  the  reason  (roC?)  bears  to  the  living 
principle  ('/'^x'?)  the  same  relation  that  the  faculty  of  vision  ip-tpis) 
bears  to  the  body  {aSifia)  :  us  yap  ev  awfiari  oxpis,  (v  ipvx^  vovs.  The 
assertion,  in  this  instance,  it  will  be  noticed,  is  that  the  relation  to 
each  other  of  the  two  former  members  of  the  analogy  is,  not  similar 
to,  but  the  same  as,  that  of  the  two  latter.  The  Aristotelian  term 
dvaXoyiay  in  fact,  exactly  corresponds  with  the  term  Proportion  as 
employed  by  mathematicians,  and  it  was  by  the  word  Proportio, 
when  not  availing  themselves  of  the  Greek  word  Analogia  itself, 
that  the  Romans  expressed  this  form  of  argument.  See  Quinctilian, 
Inst.  Oral.  i.  6 :  '  Analogi<e  quam  proxime  ex  Graeco  transferentes 
in  hatinum />roportionem  vocaverunt,  ha;c  vis  est :  Ut  id,  quod  dubium 
est,  ad  aliquid  simile,  de  quo  non  quaeritur,  referat ;  ut  incerta  certis 
probet.'  I  am  indebted  for  this  quotation  to  Mr.  Austin's  Lectures 
on  Jurisprudence  y  vol.  iii.  p.  255. 

Q  2 


228 


IMPERFECT  INDUCTIONS. 


ANALOGY, 


229 


that  I  believe  these  qualities  to  be  conjoined  invariably, 
but  that  1  know  X  and  Y  to  resemble  each  other  in  so 
many  points  that  I  believe  them  to  resemble  each  other 

in  all. 

Thus,  because  the  moon  resembles  the  earth  in  being 
a  large  spheroid  revolving  round  another  body,  as  well 
as  in  various  other  particulars,  it  may  be  argued  that 
it  probably  resembles  the  earth  also  in  sustaining  animal 
and  vegetable  life  on  its  surface.     But,  if  every  ground 
of  resemblance  furnishes  a  probable  reason  for  assigning 
to  the  one  body  any  property  known  to  belong  to  the 
other,  it  is  evident  that  every  ground  of  dissimilarity  will 
also  furnish  a  probable  reason  for  denying  of  the  first 
body  any  property  known  to  belong  to  the  second.     In 
estimating,  therefore,  the  value  of  an  analogical  argument, 
we  must  strike  a  balance  between  the  known  points  of 
resemblance  and   the   known   points  of  difference,  and 
according  as  the  one  or  the  other  preponderate,  and  in 
the  proportion  in  which  the  one  or  the  other  prepon- 
derate, is  the  weight  of  the  argument   to   be  regarded 
as  inclining.   If,  for  instance,  the  phenomenon  A  is  known 
to  resemble  the  phenomenon  B  in  four  points,  whereas 
the  known  points  of  difference  between  them  are  three, 
and  it  is  discovered  that  some  new  property  belongs  to 
A  but  it  is  uncertain  whether  it  also  belongs  to  B,  the 
value  of  the  analogical  argument  that  it  does  belong  to 
B  will  be  represented  by  4  :  3. 

Before,  however,  we  are  justified  in  drawing  this  in- 
ference, it  is  necessary  to  observe  certain  cautions. 


In  the  first  place,  we  must  have  no  evidence  that  there 
is  any  causal  connexion  between  the  new  property  and 
any  of  the  known  points  of  resemblance  or  difference. 
If  we  have  such  evidence,  the  argument  ceases  to  be 
analogical,  and,  if  not  a  perfect  induction,  is  an  imper- 
fect induction  of  the  kind  to  be  described  presently. 
We  know,  for  instance,  that  animal  and  vegetable  life  on 
the  surface  of  the  earth  could  not  exist  without  moisture  ; 
but,  so  far  as  we  are  able  to  ascertain,  there  is  no  moisture 
on  the  surface  of  the  moon.  Hence  we  appear  to  be 
justified  in  concluding,  not  by  analogy,  but  by  the  Method 
of  Difference  (assuming,  of  course,  the  accuracy  of  the 
observations),  that  animal  and  vegetable  life,  in  the  sense 
ordinarily  attached  to  those  terms,  are  not  to  be  found  on 
the  moon's  surface  ^  Again,  we  happen  to  know  two  men 
who  bear  a  considerable  resemblance  to  each  other  in 
character  and  opinions.  One  of  these  men  acts  in  a  par- 
ticular way,  and  we  infer,  analogically,  that  the  other  will 
act  similarly.  But,  suppose  we  ascertain  that  the  act  of 
the  former  man  was  due  to  some  particular  characteristic, 
say  avarice.  The  inference  will  now  no  longer  depend 
on  the  ratio  of  the  known  points  of  resemblance  to  the 
known  points  of  difference  in  the  characters  and  opinions 
of  the  two  men,  that  is,  on  analogy,  but  it  will  depend 
mainly  on  the  presence  or  absence,  the  strength  or  weak- 

*  See  the  essay  Of  the  Plurality  of  Worlds  (usually  attributed  to 
Dr.  Whewell),  ch.  ix.  sect.  7-9.  The  whole  of  this  essay  furnishes 
excellent  examples  of  the  employment  of  the  Argument  from  Analogy, 
and  also  illustrates  the  extreme  caution  and  delicacy  which  are 
requisite  in  estimating  its  value. 


230 


IMPERFECT  INDUCTIONS. 


ANALOGY, 


231 


ness,  of  this  particular  characteristic  in  the  second  man, 
and,  in  a  subsidiary  degree,  on  the  presence  or  absence, 
the  strength  or  weakness,  of  corroborating  or  counter- 
vaihng  motives  ;  that  is,  it  will  depend,  not  on  analogy, 
but  on  other  modes  of  induction. 

Secondly,  though  there  must  be  no  evidence  to  con- 
nect the  property  in  question  with  any  of  the  known 
points  of  resemblance  or  difference,  there  must,  on  the 
other  hand,  be  no  evidence  to  disconnect  it.  If  there 
be  such  evidence,  the  point  of  resemblance  or  difference 
with  which  we  know  or  believe  it  to  be  unconnected 
must,  in  estimating  the  value  of  the  analogy,  be  left  out 
of  consideration.  The  reason  is  obvious.  When  we  are 
enquiring  whether  this  property  is  more  likely  to  be 
connected  with  the  known  points  of  resemblance  or  the 
known  points  of  difference,  it  is  plain  that  we  must  only 
take  into  account  those  points  with  which  there  is,  at 
least,  some  chance  of  its  being  connected. 

Thirdly,  we  must  have  no  reason  to  suspect  that  any 
of  the  known  points  of  resemblance  or  difference,  of 
which  the  argument  takes  account,  are  causally  connected 
with  each  other.  If  the  compared  phenomena  agree  in 
the  possession  of  the  properties  a,  h,  c,  d,  e,  and  of  these 
properties  b  is  an  effect  of  (or  causally  connected  with) 
a,  and  d  is  an  effect  of  (or  causally  connected  with)  c, 
the  only  properties  which  ought  to  be  taken  into  account 
in  estimating  the  value  of  the  analogy  are  a,  c,  e.  The 
moon  is  supposed  to  differ  from  the  earth  in  having 
no  clouds  and  no  water,  but,  as  these  two  properties 


are    mutually    connected   in    the    way    of    cause    and 
effect,    they   can    only    be   allowed    to   count    as    one 
item    in   instituting    a    comparison,    for    the   purposes 
of  analogy,   between  the  known  points  of  resemblance 
and  the  known  points  of  difference  in  the  two  bodies. 
The  enormous  difference,  on  the  other  hand,  between  the 
maximum  and  minimum  temperature  of  any  place  on  the 
moon's  surface,  owing  to  the  extreme  length  of  the  lunar 
days  and  nights  and  the  absence  of  any  sensible  atmo- 
sphere, constitutes  a  distinct  point  of  difference,  and, 
as  such,   furnishes  an  additional  argument  against  the 
habitation  of  the  moon.     When  we  ask  to  which  side 
the   argument   from    analogy    inclines,   we   are   asking 
whether  it  is  more  probable  that  the  property  in  question 
(known  to  belong  to   the   one   phenomenon,   but   not 
known  either  to  belong  or  not  to  belong  to  the  other)  is 
connected,  by  way  of  causation,  with  one  of  the  known 
points  of  resemblance,  or  with  one  of  the  known  points  of 
difference :  but,  in  calculating  the  probability,  it  is  essen- 
tial that  every  point  should,  so  far  as  we  know,  be  in- 
dependent of  every  other  ;  for  it  is  only  in  virtue  of  each 
being  supposed  to  be  an  ultimate  property  or  to  point  to 
an  ultimate  property  that  it  has  any  claim  to  be  taken 
into  the  account.     Thus,  if  any  two  of  the  properties 
are  found  to  be  joint  effects  of  the  same  cause  or  to 
stand  to  each  other  in  the  relation  of  cause  and  effect, 
they  furnish  only  one  argument  instead  of  two.     If  we 
say  of  A  that  he  is  likely,  under  some  particular  con- 
juncture of  circumstances,  to  act  in  the  same  manner  as 


232 


IMPERFECT  INDUCTIONS, 


B,  because  they  are  both  of  them  vain  and  selfish,  we 
shall  not  strengthen  our  argument  by  adding  a  number 
of  characteristics  which  are  deducible  from  vanity  and 
selfishness,  or  by  adducing  a  number  of  individual  acts 
in  which  these  qualities  have  been  exhibited. 

Fourthly,  it  is  only  when  we  have  reason  to  suppose 
that  we  are  acquainted  with  a  considerable  proportion  of 
the  properties  of  two  objects,  that  the  argument  from 
analogy  can  have  much  weight.  If  we  know  only  a  few 
properties  out  of  a  large  number,  they  may  happen  to  be 
precisely  those  which  are  exceptional  rather  than  repre- 
sentative, points  of  similarity  where  the  objects  them- 
selves are  mainly  dissimilar,  or  points  of  dissimilarity 
where  the  objects  are  mainly  similar.  Thus,  we  know 
that  in  some  respects  the  planet  Mars  closely  resembles 
the  earth,  as,  for  instance,  in  having  an  atmosphere, 
a  surface  distributed  into  land  and  water,  and  probably 
a  temperature  in  which  life  similar  to  that  on  our  own 
globe  might  exist  :  but  it  would  be  very  rash  to  conclude 
from  these  data  that  it  also  resembles  the  earth  in  sus- 
taining animal  and  vegetable  life  on  its  surface;  for, 
though  life,  such  as  we  understand  it,  does  not  appear 
to  be  impossible  on  the  planet  Mars  as  it  appears  to  be 
on  many  of  the  other  celestial  bodies,  the  number  of 
properties  with  which  we  are  acquainted  is  so  small  as 
compared  with  the  number  of  properties  with  which  we 
are  unacquainted  that  there  is  little  or  nothing  on  which 
to  ground  even  a  probable  conclusion.  On  the  other 
hand,  the  analogy  by  which  Kepler  boldly  extended  the 


ANALOGY. 


^33 


three  laws  gained  from  the  observation  of  the  motion 
of  Mars  to  the  remaining  planets  was  a  perfectly  sound 
one  ;  for  the  orbit  of  a  planet,  as  compared  with  the 
condition  of  its  surface,  is  a  very  simple  phenomenon, 
and  what  was  known  of  the  orbits  of  the  other  planets 
made  it  appear  more  likely  that  they  would  correspond 
with  the  orbit  of  Mars  than  that  they  would  differ 
from  it. 

The  value  of  the  Argument  from  Analogy,  then,  we 
see,  depends  on  the  ratio  of  the  ascertained  points  of 
resemblance  to  (i)  the  ascertained  points  of  difference, 
(2)  the  entire  assemblage  of  the  properties  of  the  ob- 
jects compared.  If  the  ascertained  resemblances  are 
numerous,  the  ascertained  differences  few,  and  we  have 
reason  to  think  that  we  are  well  acquainted  with  the 
objects  compared,  the  argument  from  analogy  is  very 
forcible.  If,  on  the  other  hand,  the  ascertained  resem- 
blances only  slightly  exceed  in  number  the  ascertained 
differences,  or  if  we  have  reason  to  suppose  that  there 
are  numerous  properties  in  the  compared  objects  with 
which  we  are  unacquainted,  the  value  of  the  argument 
from  analogy  may  be  very  slight.  It  is  commonly  said 
that  the  value  of  an  argument  from  analogy  ranges  from 
certainty  to  zero.  If  it  reaches  certainty,  the  argument 
becomes  a  complete  induction ;  if  it  falls  to  zero,  it 
ceases  to  be  an  argument  at  all ;  if  the  probability  is 
expressed  by  less  than  one-half,  that  is,  if  the  number 
of  ascertained  resemblances  be  less  than  the  number 
of  ascertained  differences,  it  is  usual  to  say  that  analogy 


234 


IMPERFECT  INDUCTIONS, 


is  against  the  possession  by  the  one  object  of  a  quality 
known  to  belong  to  the  other,  or,  in  other  words,  in 
favour  of  their  differing  in  the  possession  of  this  quahty 
rather  than  agreeing  in  it. 

*  Besides  the  competition  between  analogy  and  diver- 
sity,' says  Mr.  MilP,  'there  may  be  a  competition  of 
conflicting  analogies.'  An  object  may  be  known  to 
resemble  one  object  in  some  particulars  and  another  in 
others,  and  it  may  be  a  question  with  which  of  the  two 
it  ought  to  be  classed,  or  which  of  the  two  it  is  the  more 
likely  to  resemble  in  some  unknown  property.  Thus, 
for  some  time  it  was  a  question  whether  a  sponge  was 
an  animal  or  a  vegetable  substance ;  and  it  is  often  by 
conflicting  analogies  that  we  attempt  to  determine  to 
which  of  two  or  more  masters  a  painting  or  a  statue 
should  be  ascribed. 

The  extreme  caution  which  is  requisite  in  employing  the 
Argument  from  Analogy  may  be  illustrated  by  the  follow- 
ing scientific  errors  which  have  resulted  from  a  hasty  and 
inconsiderate  employment  of  this  mode  of  reasoning. 

Sir  W.  Grove,  in  his  Correlation  of  Physical  Forces  ^^ 
while  combating  the  once  fashionable  doctrine  of  elec- 
trical fluids,  brings  into  juxta-position  two  very  interest- 
ing instances  of  hasty  analogies. 

*The  progressive  stages,'  he  says,  '  in  the  History  of  Phy- 
sical Philosophy  will  account  in  a  great  measure  for  the 
adoption  by  the  early  electricians  of  the  theories  of  fluids. 

•  Mill's  Logic,  Bk.  III.  ch.  xx.  §  2. 
»"  Fifth  edition,  p.  135. 


ANALOGY, 


'^^^ 


*  The  ancients,  when  they  witnessed  a  natural  phenomenon, 
removed  from  ordinary  analogies,  and  unexplained  by  any 
mechanical  action  known  to  them,  referred  it  to  a  soul,  a 
spiritual  or  preternatural  power  :  thus  amber  and  the  magnet 
were  supposed  by  Thales  to  have  a  soul ;  the  functions  of 
digestion,  assimilation,  &c.,  were  supposed  by  Paracelsus  to 
be  effected  by  a  spirit  (the  Archaeus).  Air  and  gases  were 
also  at  first  deemed  spiritual,  but  subsequently  became 
invested  with  a  more  material  character;  and  the  word 
gas,  from  geist^  a  ghost  or  spirit,  affords  us  an  instance  of 
the  gradual  transmission  of  a  spiritual  into  a  physical 
conception. 

*  The  establishment  by  Torricelli  of  the  ponderable  char- 
acter of  air  and  gas,  showed  that  substances  which  had  been 
deemed  spiritual  and  essentially  different  from  ponderable 
matters  were  possessed  of  its  attributes.  A  less  superstitious 
mode  of  reasoning  ensued,  and  now  aeriform  fluids  were 
shown  to  be  analogous  in  many  of  their  actions  to  liquids  or 
known  fluids.  A  belief  in  the  existence  of  other  fluids, 
differing  from  air  as  this  differed  from  water,  grew  up,  and, 
when  a  new  phenomenon  presented  itself,  recourse  was  had 
to  a  hypothetic  fluid  for  explaining  the  phenomenon  and  con- 
necting it  with  others ;  the  mind,  once  possessed  of  the  idea 
of  a  fluid,  soon  invested  it  with  the  necessary  powers  and 
properties,  and  grafted  upon  it  a  luxuriant  vegetation  of 
imaginary  offshoots.' 

Most  of  my  readers  will  be  aware  of  the  difficulties 
experienced  by  the  early  geologists  in  accounting  for 
the  fact  that  the  strata  of  our  own  and  other  northern 
countries  often  contain  remains  of  animals  and  shells 
akin  to  those  which  are  now  to  be  found  only  in  the 
torrid  zone.  This  difficulty  is  easily  explained  by  sup- 
posing a  different  distribution  of  land  and  water  over  the 


ITjS  IMPERFECT  INDUCTIONS. 

surface  of  the  globe  from  that  which  at  present  exists. 
But  we  must  pause  before  we  admit  the  inference  that, 
because  these  animals  and  shells  are  akin  to  those  which 
are  now  found  only  in  warm  climates,  they  must,  there- 
fore, have  subsisted  in  a  similar  temperature. 

*  When  reasoning  on  such  phenomena,'  says  Sir  Charles 
Lyell  'S  '  the  reader  must  always  bear  in  mind  that  the  fossil 
individuals  belonged  to  species  of  elephant,  rhinoceros,  hippo- 
potamus, bear,  tiger,  and  hyaena,  distinct  from  those  which 
now  dwell  within  or  near  the  tropics.  Dr.  Fleming,  in  a 
discussion  on  this  subject,  has  well  remarked  that  a  near 
resemblance  in  form  and  osteological  structure  is  not  always 
followed,  in  the  existing  creation,  by  a  similarity  of  geo- 
graphical distribution  ;  and  we  must  therefore  be  on  our 
guard  against  deciding  too  confidently,  from  mere  analogy  of 
anatomical  structure,  respecting  the  habits  and  physiological 
peculiarities  of  species  now  no  more.  "  The  zebra  delights  to 
roam  over  the  tropical  plains ;  while  the  horse  can  maintain 
its  existence  throughout  an  Iceland  winter.  The  buffalo,  like 
the  zebra,  prefers  a  high  temperature,  and  cannot  thrive  even 
where  the  common  ox  prospers.  The  musk  ox,  on  the  other 
hand,  though  nearly  resembling  the  buffalo,  prefers  the  stinted 
herbage  of  the  arctic  regions,  and  is  able,  by  its  periodical 
migrations,  to  outlive  a  northern  winter.  The  jackal  {Canis 
aureus)  inhabits  Africa,  the  warmer  parts  of  Asia,  and 
Greece  ;  while  the  isatis  {Cams Itigopus)  r^sxd^s  in  the  arctic 
regions.  The  African  hare  and  the  polar  hare  have  their 
geographical  distribution  expressed  in  their  trivial  names  ;  " 
and  different  species  of  bears  thrive  in  tropical,  temperate, 
and  arctic  latitudes. 

*  Recent  investigations  have  placed  beyond  all  doubt  the 

•^  LycU's  Principles  of  Geology,  ch.  vi.  (ninth  edition) ;   ch.   x. 
(tenth  edition). 


INCOMPLETE  INDUCTIONS. 


'^Zl 


important  fact  that  a  species  of  tiger,  identical  with  that  of 
Bengal,  is  common  in  the  neighbourhood  of  Lake  Aral,  near 
Sussac,  in  the  forty-fifth  degree  of  north  latitude ;  and  from 
time  to  time  this  animal  is  now  seen  in  Siberia,  in  a  latitude 
as  far  north  as  the  parallel  of  Berlin  and  Hamburgh.  Hum- 
boldt remarks  that  the  part  of  Southern  Asia  now  inhabited 
by  this  Indian  species  of  tiger  is  separated  from  the  Hima- 
laya by  two  great  chains  of  mountams,  each  covered  with 
perpetual  snow,— the  chain  of  Kuenlun,  lat.  35°  N.,  and  that 
of  Mouztagh,  lat.  42°,— so  that  it  is  impossible  that  these 
animals  should  merely  have  made  excursions  from  India,  so 
as  to  have  penetrated  in  summer  to  the  forty-eighth  and  fifty- 
third  degrees  of  north  latitude.  They  must  remain  all  the 
winter  north  of  the  Mouztagh,  or  Celestial  Mountains.  The 
last  tiger,  killed  in  1828,  on  the  Lena,  in  lat.  521°,  was  in  a 
climate  colder  than  that  of  Petersburg  and  Stockholm.' 

Neither  through  Analogy  nor  through  Induction  by 
Simple  Enumeration  can  we  establish  a  fact  of  Causa- 
tion, though  the  conclusions  of  either  of  these  methods 
may  suggest  to  us  such  a  fact.  When  we  begin  to 
suspect  that  any  one  circumstance  or  set  of  circum- 
stances is  the  cause  or  the  effect  of  another,  or  con- 
nected with  it  in  the  way  of  causation,  we  ought  at  once 
to  attempt  to  apply,  if  possible,  one  or  more  of  the 
Experimental  Methods.  If  we  can  satisfy  ourselves  that 
their  conditions,  or  those  of  any  one  of  them,  have  been 
rigorously  fulfilled,  we  have,  of  course,  obtained  a  Valid 
Induction,  giving  us  either  absolute  or  moral  certainty. 
But  something  considerably  short  of  a  rigorous  fulfilment 
of  these  conditions  may  still  lead  to  a  conclusion,  pos- 
sessing more  or  less  of  probability.      We  may,  for  in- 


238 


IMPERFECT  INDUCTIONS. 


stance,  to  take  the  Method  of  Agreement,  feel  uncertain 
whether  a  and  b  (any  two  circumstances)  are  the  only 
material  circumstances  which  the  cases  we  have  examined 
exhibit  in  common  ;  but  still  we  may  have  examined  so 
many,  so  various,  and  so  well  selected  instances,  that  we 
may  be  justified  in  regarding  it  as  highly  probable  that 
the  two  circumstances  stand  to  each  other  in  the  relation 
of  cause  and  effect,  or  are,  at  least,  connected  in  the 
way  of  causation.      Similarly,  to  take  the  Method    of 
Difference,  in  the  act  of  introducing  a  new  antecedent, 
we  may   have  unwittingly  introduced   some  other  new 
antecedent,  or,  in  omitting  an  antecedent,  we  may  have 
unwittingly  introduced  or  omitted  some  other  antecedent ; 
but  still  we  may  have  exercised  such  extreme  caution 
as  to  justify  us  in  feeling  an  assurance  amounting  almost, 
though  not  altogether,  to  certainty  that  the  experiment 
has  been  rightly  performed.      The  less   our  assurance 
of  this  fact,  the  slighter  is  the  probability  of  the  con- 
clusion. 

There  remains  one  case,  which  is  attended  with  some 
perplexity.  It  sometimes  happens  that,  though  we  may 
be  unable  to  establish  a  fact  of  causation  between  two 
particular  phenomena,  we  may  be  able  to  show  that  some 
one  phenomenon  stands  in  a  causal  relation  to  some 
one  or  other  of  a  definite  number  of  other  phenomena. 
Thus,  supposing  a  vegetable  to  be  transplanted  to  a 
distant  part  of  the  world,  we  may  be  able  to  assure 
ourselves,  by  excluding  other  causes  of  difference,  that 


INCOMPLETE  INDUCTIONS, 


239 


any  new  qualities  which  it  may  assume  are  due  either 
to  difference  of  climate,  or  to  difference  of  soil,  or  to 
both  these  causes  conjointly,  though  our  knowledge  may 
not  enable  us  to  assign  amongst  these  alternatives  the 
particular  cause  or  combination  of  causes  to  which  the 
effect   is   due.     Now   ought   such   an    Inference  to  be 
classified  as  a  perfect  or  an  imperfect  Induction?      If 
we  content  ourselves  with  stating  the  alternatives,  the 
inference  should   be  regarded,  so  far  as  it  goes,  as  a 
Perfect  Induction  ;  for  within  the  limits  stated  the  con- 
clusion may  be  considered  absolutely  certain.     But  if, 
on  any  grounds,  we  suppose  one  of  these  alternatives 
to  be  more  probable  than  the  others,  and  we  state  this  as 
our  conclusion,  the  inference  is,  of  course,  only  a  pro- 
bable one,  and  should  rank  as  an  Imperfect  Induction. 

The  same  remarks  will  apply  to  those  cases  in  which 
there  is  any  uncertainty  as  to  the  nature  of  the  fact  of 
causation.  If  the  inference  be,  say,  that  the  two  pheno- 
mena either  are  one  cause  and  the  other  effect,  or  stand 
to  each  other  in  the  relation  of  cause  and  effect,  though 
we  may  be  unable  to  determine  which  of  the  two  is 
cause  and  which  is  effect,  or  are  both  of  them  effects  of 
the  same  cause  (adding  any  other  alternatives  which  the 
particular  case  may  require),  the  inference  is,  so  far  as  it 
goes,  a  Perfect  Induction.  But,  if  one  or  some  only  of 
these  alternatives  be  selected,  on  any  grounds  short  of 
absolute  or  moral  certainty,  to  the  exclusion  of  the 
others,  the  inference  is  only  probable,  and  must  be  re- 
garded as  merely  an  Imperfect  Induction. 


240 


IMPERFECT  INDUCTIONS, 


Briefly  to  sum  up  the  contents  of  this  chapter,  Im- 
perfect Inductions  are  the  results  either  of  an  Inductio 
per  Enumerationem  SimpHcem  (to  which  I  propose  to 
appropriate  the  expression  *  Empirical  Generalisations  '), 
or  of  the  Argument  from  Analogy  (which  I  call  Ana- 
logies), or  of  an  imperfect  fulfilment  of  one  or  other 
of  the  Inductive  Methods  (to  which  we  might,  perhaps, 
advantageously  appropriate  the  expression  'Incomplete 
Inductions  ').  In  the  two  former  cases  there  can  be  no 
more  than  an  intimation  of  a  Fact  of  Causation,  while  in 
the  last  we  conceive  ourselves  to  be  on  the  way  towards 
establishing  one. 


CHAPTER  V. 


On  the  relatiojt  of  Induction  to  Deduction^ 
and  on  Verification, 

THE  results  of  our  inductions  are  summed  up  in 
general  propositions,  which  are  not  unfrequently  stated 
in  the  shape  of  mathematical  formulae.  These  general 
propositions,  the  results  of  inductive  reasoning,  become, 
in  turn,  the  data  from  which  deductive  reasoning  pro- 
ceeds. Though  the  major  premiss  of  any  single  deduc- 
tive argument  may  itself  be  the  result  of  deduction,  it 
will  invariably  be  found,  as  pointed  out  long  ago  by 
Aristotle',  that  the  ultimate  major  premiss  of  a  chain 
of  deductive  reasoning  is  a  result  of  induction.  There 
must  be  some  limit  to  the  generality  of  the  propositions 
under  which  our  deductive  inferences  can  be  subsumed, 
and,  when  we  have  reached  this  limit,  the  only  evidence 
on  which  the  ultimate  major  premiss  can  repose,  if  it 
depend  on  evidence  at  all,  must  be  inductive.  Thus, 
most  of  the  deductions  in  the  science  of  Astronomy,  and 

^  'H  yi\v  5^  67ra7(V7^  "/'X'7  **'"''*  '^<**  '^°'^  KaOoKov,  6  5^  cvWoyifffibs 
(K  TMv  KaOuKov.  Eiaiv  dpa  dpxal  ($  Siv  6  avK\oyi(T^ds,  Sjv  ovk  effri 
avWoyicffios-  fvayojy^  dpa. — Etk.  Nic.  vi.  3  (3).  Cp.  Eth,  Nic.  vi. 
6,  8  (9)  ;  Metaphysics,  i.  i  ;  Posterior  Analytic s,  ii.  19. 


242  RELATION  OF  INDUCTION  TO  DEDUCTION, 

many  of  those  in  the  science  of  Mechanics,  depend 
ultimately  on  the  Law  of  Universal  Gravitation;  but 
this  Law  itself  is  the  result  of  an  induction  based  upon 
a  variety  of  facts,  including  both  the  fall  of  bodies  to 
the  earth  and  the  motion  of  the  planets  in  their  orbits. 
Again,  a  large  number  of  geometrical  deductions  may 
be  traced  up  to  the  ultimate  major  premiss:  *  Things 
that  are  equal  to  the  same  thing  are  equal  to  one  an- 
other.' But  this  proposition,  if  not  referred  directly  to 
induction,  is  classed  under  the  head  of  intuitive  con- 
ceptions, the  most  probable,  though  perhaps  not  the 
most  commonly  received,  explanation  of  which  is  that 
which  derives  them  from  the  accumulated  experience  of 
generations,  transmitted  hereditarily  from  father  to  son. 

A  Deductive  Inference  combines  the  results  of  pre- 
vious inductions  or  deductions,  and  evolves  new  pro- 
positions as  the  consequence,  or,  to  put  the  matter  in 
a  slightly  different  point  of  view,  as  expressing  the  total 
result,  of  these  combinations.  I  append  a  few  easy  ex- 
amples of  the  manner  in  which  the  results  of  induction 
are  employed  in  a  deductive  argument. 

To  begin  with  a  very  simple  instance,  but  one  which 
will  serve  as  a  good  illustration  of  the  stage  at  which 
our  investigations  cease  to  be  inductive  and  become 
deductive; — suppose  we  have  ascertained,  by  previous 
inductions,  that  A  produces  a,  B  produces  ^,  C  pro- 
duces -5,  D  produces  ^,  and  E  produces  |,  we  know, 
by  calculation — that  is,  by  deductive  reasoning — that  the 
total  effect  of  A,  B,  C,  D,  E  is  i$-^%      In  this  case 


AND    VERIFICATION, 


243 


the  simple  rules  of  Algebra,  governing  the  addition  and 
subtraction  of  quantities,  combined  with  the  special 
data  here  furnished,  are  the  premisses  from  which  our 
deductive  reasoning  proceeds. 

The  proposition  proved  in  Euclid,  Book  i.  Prop.  38, 
that  *  Triangles  upon  equal  bases,  and  between  the  same 
parallels,  are  equal  to  one  another,'  is  derived  from,  or 
is  the  total  result  of,  the  previous  deductions  (i)  that 
*  Parallelograms  upon  equal  bases,  and  between  the  same 
parallels,  are  equal  to  one  another,'  (2)  that  *  Triangles 
formed  by  the  diagonal  of  a  parallelogram  are  each  of 
them  equal  to  half  the  parallelogram  '  (i.  34),  and  (3)  the 
previous  induction  that  '  the  halves  of  equal  things  are 
equal.' 

What  is  called  the  Hydrostatic  Paradox,  namely,  that 
a  man  standing  on  the  upper  of  two  boards,  which  form 
the  ends  of  an  air-tight  leather  bag,  and  blowing  through 
a  small  tube  opening  into  the  space  between  the  board, 
can  easily  raise  his  own  weight,  is  a  combination  of  two 
propositions,  both  gained  from  experience  by  means  of 
induction,  these  propositions  being  (i)  that  fluids  trans- 
mit pressure  equally  in  all  directions,  (2)  that,  the  greater 
the  pressure  brought  to  bear  on  any  surface  from  below, 
the  greater  the  weight  which  it  will  sustain  (otherwise  ex- 
pressed by  the  Mechanical  Law  that  action  and  reaction 

are  equal). 

To  take  another  very  simple  instance  of  a  similar  kind. 
One  of  the  earliest  and  easiest  problems  in  the  Science 
of  Optics  is  the  following  :  *  A  conical  pencil  of  rays  is 

R  2 


244  RELATION  OF  INDUCTION  TO  DEDUCTION, 

incident  upon  a  plane  reflecting  surface  ;  to  determine 
the  form  of  the  reflected  pencil.'  The  solution,  that  the 
reflected  pencil  will  be  a  cone  having  for  its  vertex 
a  certain  imaginary  point,  which  can  be  geometrically 
determined,  on  the  other  side  of  the  surface,  is  derived 
from  a  combination  of  the  experimental  truth,  gained 
by  induction,  that  'the  angle  of  reflexion  is  equal  to 
the  angle  of  incidence  '  with  the  geometrical  propositions 
stated  in  Euclid  i.  8  and  i.  29. 

In  the  Science  of  Political  Economy,  Ricardo's  Theory 
of  Rent,  when  stated  in  the  slightly  modified  form  that 
*  the  rent  of  land  represents  the  pecuniary  value  of  the 
advantages  which  such  land  possesses  over  the  least 
valuable  land  in  cultivation,'  is  an  easy  deduction  from 
two  principles  which  are  supplied  by  every  one's  experi- 
ence, namely,  (i)  that  land  varies  in  value,  and  (2)  that 
there  is  some  land  either  so  bad  or  so  disadvantageously 
situated  as  to  be  not  worth  the  cultivating  ^ 

Professor  Cairnes'  work  on  the  Slave  Power  furnishes 
a  remarkable  example  of  the  successful  application  of  the 
deductive  method  to  the  determination  of  economical 
questions.  The  economical  effects  of  slavery  are  thus 
traced.  We  learn  from  observation  and  induction  that 
slave  labour  is  subject  to  certain  characteristic  defects : 


*  The  student  will  find  an  easy  exposition  of  this  Theory  in 
Fawcett's  Manual  of  Political  Economy,  Bk.  II.  ch.  iii.  ad  init.  As 
originally  stated,  Ricardo's  theory  neglected  to  take  account  of  ad- 
vantages of  situation,  such  as  proximity  to  a  market,  and  regarded 
the  value  of  land  as  depending  solely  on  its  fertility. 


AND    VERIFICATION, 


245 


it  is  given  reluctantly ;  it  is  unskilful ;  and,  lastly,  it  is 
wanting  in  versatility.  As  a  consequence  of  these  cha- 
racteristics, it  can  only  be  employed  with  profit  when  it 
is  possible  to  organise  it  on  a  large  scale.  It  requires 
constant  supervision,  and  this  for  small  numbers  or 
for  dispersed  workmen  would  be  too  costly  to  be  re- 
munerative. The  slaves  must,  consequently,  be  worked 
in  large  gangs.  Now  there  are  only  four  products  which 
repay  this  mode  of  cultivation,  namely,  cotton,  sugar, 
tobacco,  and  rice.  Hence  a  country  in  which  slave 
labour  prevails  is  practically  restricted  to  these  four 
products,  for  it  is  another  characteristic  of  slave  labour, 
under  its  modern  form,  that  free  labour  cannot  exist 
side  by  side  with  it.  But,  besides  restricting  cultivation 
to  these  four  products,  some  or  all  of  which  have  a 
peculiar  tendency  to  exhaust  the  soil,  slave  labour,  from 
its  want  of  versatility,  imposes  a  still  further  restriction. 
*  The  difficulty  of  teaching  the  slave  anything  is  so  great 
— the  result  of  the  compulsory  ignorance  in  which  he  is 
kept,  combined  with  want  of  intelligent  interest  in  his 
work — that  the  only  chance  of  rendering  his  labour 
profitable  is,  when  he  has  once  learned  a  lesson,  to  keep 
him  to  that  lesson  for  life.  Accordingly,  where  agricul- 
tural operations  are  carried  on  by  slaves,  the  business  of 
each  gang  is  always  restricted  to  the  raising  of  a  single 
product.  Whatever  crop  be  best  suited  to  the  character 
of  the  soil  and  the  nature  of  slave  industry,  whether 
cotton,  tobacco,  sugar,  or  rice,  that  crop  is  cultivated, 
and  that  crop  only.     Rotation  of  crops  is  thus  precluded 


246  RELATION  OF  INDUCTION  TO  DEDUCTION, 

by  the  conditions  of  the  case.  The  soil  is  tasked  again 
and  again  to  yield  the  same  product,  and  the  inevitable 
result  follows.  After  a  short  series  of  years  its  fertility 
is  completely  exhausted,  the  planter  abandons  the  ground 
which  he  has  rendered  worthless,  and  passes  on  to  seek 
in  new  soils  for  that  fertility  under  which  alone  the 
agencies  at  his  disposal  can  be  profitably  employed.' 
Thus,  from  the  characteristics  of  slave  labour  may  be 
deduced  the  economical  effect  of  exhaustion  of  the  soil 
on  which  it  prevails,  and  the  consequent  necessity  of 
constantly  seeking  to  extend  the  area  of  cultivation. 
From  the  peculiar  character  of  the  crops  which  can^ 
alone  be  successfully  raised  by  slave  labour  may  be  ex- 
plained the  former  prevalence  of  slavery  in  the  Southern, 
and  its  absence  in  the  Northern,  States  of  the  American 
Union  ;  and  from  the  necessity  of  constantly  seeking 
fertile  virgin  soil  for  the  employment  of  slave  labour  may 
be  explained  the  former  policy  of  the  Southern  States, 
which  was  invariably  endeavouring  to  bring  newly  consti- 
tuted States  under  the  dominion  of  slave  institutions'. 

These  examples  of  the  combination  of  inductive  with 
deductive  reasoning  might  be  multiplied  to  any  extent. 
Mechanics,  Astronomy,  and  the  Mathematico-physical 
sciences  generally,  furnish,  perhaps,  the  most  striking 
instances  of  it.  The  great  importance  of  deduction  as 
an  instrument  for  the  ascertainment  of  physical  truths 

3  See  Professor  Caimes  on  the  Slave  Pmver,  ch.  ii.  His  arguments 
are  stated  in  a  condensed  form  in  Fawcett's  Manual  of  Political 
Economy^  Bk.  II.  ch.  xi. 


AND    VERIFICATION. 


247 


could  hardly  be  illustrated  more  appropriately  than  by 
the  following  cases  adduced  by  Sir  John  Herschel  * : — 

*  It  had  been  objected  to  the  doctrine  of  Copernicus,  that, 
were  it  true,  Venus  [and,  it  might  have  been  added,  Mer- 
cury, as  the  other  inferior  planet]  should  appear  sometimes 
horned  like  the  moon.  To  this  he  answered  by  admitting  the 
conclusion,  and  averring  that,  should  we  ever  be  able  to  see 
its  actual  shape,  it  would  appear  so.  It  is  easy  to  imagine 
with  what  force  the  application  would  strike  every  mind  when 
the  telescope  confirmed  this  prediction,  and  showed  the 
planet  just  as  both  the  philosopher  and  his  objectors  had 
agreed  it  ought  to  appear.  The  history  of  science  affords 
perhaps  only  one  instance  analogous  to  this.  When  Dr. 
Hutton  expounded  his  theory  of  the  consolidation  of  rocks  by 
the  application  of  heat,  at  a  great  depth  below  the  bed  of  the 
ocean,  and  especially  of  that  of  marble  by  actual  fusion  ;  it  was 
objected  that,  whatever  might  be  the  case  with  others,  with 
calcareous  or  marble  rocks,  at  least,  it  was  impossible  to 
grant  such  a  cause  of  consolidation,  since  heat  decomposes 
their  substance  and  converts  it  into  quicklime,  by  driving  off 
the  carbonic  acid,  and  leaving  a  substance  perfectly  infusible, 
and  incapable  even  of  agglutination  by  heat.  To  this  he 
replied,  that  the  pressure  under  which  the  heat  was  applied 
would  prevent  the  escape  of  the  carbonic  acid  ;  and  that 
being  retained,  it  might  be  expected  to  give  that  fusibility  to 
the  compound  which  the  simple  quicklime  wanted.  The 
next  generation  saw  this  anticipation  converted  into  an 
observed  fact,  and  verified  by  the  direct  experiments  of  Sir 
James  Hall,  who  actually  succeeded  in  melting  marble,  by 
retaining  its  carbonic  acid  under  violent  pressure.' 

It  should  be  noticed  that,  for  the  most  part,  in  the 
actual  conduct  of  scientific  enquiry,  there  is  a  constant 

*  Discourse  on  the  Study  of  Nattval  Philosophy,  §  299. 


248  RELATION  OF  INDUCTION  TO  DEDUCTION, 

alternation  of  the  processes  of  Induction  and  Deduction. 
A  truth  obtained  inductively  is  often  at  once  used,  either 
by  itself  or  in  combination  with  other  propositions,  for 
the  purpose  of  evolving  new  truths  by  deduction,  while  it 
may  also  be  subsequently  employed  together  with  other 
inductions  of  the  same  order  for  the  purpose  of  leading 
up  inductively  to  propositions  of  a  higher  degree  of 
generality.  We  are  constantly  passing  from  the  one 
process  to  the  other,  and  back  again,  and  often  it  be- 
comes exceedingly  difficult  to  determine  exactly  how 
much  of  our  ultimate  conclusion  is  due  to  the  one  method, 
and  how  much  to  the  other.  It  is  an  error  (though  this 
error  has  received  the  countenance  of  Bacon)  to  suppose 
that  the  process  of  induction  should  always  be  pursued 
continuously  up  to  a  certain  point,  and  that  from  that 
point  the  process  of  deduction  should  proceed  equally 
uninterruptedly.  We  may,  and  in  fact  should,  frequently 
pause  to  consider  to  what  deductive  conclusions  our  in- 
ductive inferences  lead,  or  to  try  whether  they  may  not 
be  connected  by  a  chain  of  deductive  reasoning  with 
wider  truths  previously  ascertained  \ 

A  very  common  instance  of  the  constant  interlacing  of 
the  inductive  and  deductive  processes  just  noticed  is  to 
be  found  in  the  ordinary  mode  of  framing  and  employing 
hypotheses.  First,  our  hypotheses  are  always  suggested 
by  some  fact,  or  facts,  within  our  experience.  They  are 
thus  based  on  a  rough  kind  of  induction.    When  framed, 

'  On  this  subject,  see  the  excellent  criticism  on  Bacon  in  Mr. 
Mill's  Logic,  Bk.  VI.  ch.  v.  §  5. 


AND    VERIFICATION, 


249 


we  generally  proceed  to  trace  the  consequences  which 
would  ensue  on  the  supposition  of  their  truth.  This  is 
a  deductive  process.  Individual  facts  or  inductions  from 
individual  facts  are  then  compared  with  these  results, 
and,  if  they  agree  with  them,  are  regarded  as  confirmatory 
of  the  hypothesis.  Of  course,  these  processes  may  be 
frequently  repeated,  and  are  often  so  repeated,  the  hypo- 
thesis thus  constantly  gaining  in  probability,  even  though 
it  may  as  yet  have  no  claim  to  be  regarded  as  an  esta- 
blished truth.  Lastly,  if  it  attain  the  position  of  a  valid 
induction,  it  must  be  by  the  application  of  one  or  other 
of  the  inductive  methods,  which  converts  its  previous  pro- 
bability into  scientific  certainty.  Or,  perhaps,  it  may  be 
finally  established  not  by  induction  at  all,  but  by  being 
brought  deductively  under  some  more  general  law. 


These  remarks  and  the  instances  adduced  above  natu- 
rally lead  to  a  discussion  of  the  place  to  be  assigned  in 
scientific  enquiry  to  the  process  called  Verification.  In 
Deductive  Reasoning,  especially  when  it  involves  ela- 
borate calculations,  there  is  always  great  danger  lest  we 
should  have  omitted  to  take  into  account  some  particular 
agency  or  element,  or  have  miscalculated  its  effects,  or 
have  formed  a  false  estimate  of  the  combined  effect  of 
the  various  agencies  or  elements  in  operation.  The  only 
remedy  against  these  possible  errors,  besides  the  employ- 
ment of  great  caution  in  the  conduct  of  the  deductive 
process  itself,  is  to  be  found  in  Verification,  a  word  which, 


250     RELA  TION  OF  IND UCTION  TO  DED UCTION, 

in  its  stricter  sense,  appears  to  be  applied  to  the  process 
of  testing,  by  means  of  an  appeal  to  facts,  the  validity  of 
the  conclusions  already  arrived  at  by  a  course  of  deduc- 
tive reasoning.     Thus  it  had  been  deductively  inferred 
from  the  Copernican  theory  that  the  planets  Venus  and 
Mercury  ought  to  pass  through  phases,  like  the  moon, 
and  the  application  of  the  telescope,  by  means  of  which 
they  were  actually  seen  to  assume  these  phases,  furnished 
a  triumphant  verification  of  the  inference.     Every  occur- 
rence of  an  eclipse  of  the  sun  or  moon  or  of  the  transit 
or  occultation  of  a  star,  when  it  accords  with  the  previous 
calculations  of  astronomers,  is  also  an  instance  of  Verifi- 
cation in  this,  the  stricter,  sense  of  the  term.     The  dis- 
covery  of  the    planet    Neptune    affords    an    excellent 
instance  of  the  same  kind.     But  the  word  is  often  used 
in  a  looser  sense  and  extended  to  all  cases  in  which  an 
appeal  is  made  to  facts,  as,  for  instance,  when  we  perform 
an  experiment  in  order  to  test  the  truth  of  a  hypothesis, 
or  where  we  employ  the  Method  of  Difference  in  order 
to  supplement  the  characteristic  uncertainty  attaching  to 
the  employment  of  the  Method  of  Agreement.     Of  the 
process  denoted  by  this  looser  sense  of  the  word,  in- 
stances will   readily  occur   to   every   one.      Thus,    the 
diminution  in  the  periods  of  Encke's  comet  has  been 
regarded  by  some  astronomers  (though,  perhaps,  errone- 
ously) as  a  verification  of  the  theory  that  space  is  filled 
with  an  interstellar  medium ;    or,  to  take  an  instance 
from  a  very  different  class  of  subjects,  the  recent  break- 
ing-up  of  the  slave-system   in   the  Southern  States   of 


AND    VERIFICATION, 


251 


America  may  be  regarded  as  a  verification  of  the  pre- 
diction that  slave  and  free  institutions  could  not  long 
co-exist  under  the  same  political  form  of  government. 
For  an  instance  of  a  case  in  which  the  Method  of  Dif- 
ference is  called  in  to  verify  a  previous  employment  of 
the  Method  of  Agreement,  I  may  refer  back  to  the 
enquiry  into  the  cause  of  crystallization,  already  adduced 
in  my  discussion  of  those  two  methods  ^ 

There  is  a  still  wider  application  of  the  word  Veri- 
fication, by  which  it  is  extended  to  any  corroboration  of 
one  mode  of  proof  by  means  of  another.  It  thus  in- 
cludes a  deductive  proof  adduced  in  corroboration  of  an 
inductive  one.  The  most  common  instance  of  this  kind 
of  verification  is  the  inclusion  of  a  partial  under  a  more 
general  law,  the  partial  law  having  been  arrived  at  induc- 
tively, and  it  being  subsequently  shown  that  the  more 
general  law  leads  deductively  to  it.  Thus,  the  phenomena 
of  the  Tides  had,  prior  to  the  epoch  of  Newton,  been 
partially  explained  by  the  inductive  method.  Newton, 
by  deducing  these  phenomena  from  the  Law  of  Universal 
Gravitation,  not  only  afforded  a  much  more  complete 
explanation,  but  also  furnished  the  most  convincing 
verification  of  the  results  already  arrived  at.  Similarly, 
the  laws  of  falling  bodies  on  the  earth's  surface,  which 
had  already  been  proved  inductively,  were,  from  the  time 
of  Newton,  brought  under  the  law  of  universal  gravita- 
tion, and  proved  deductively  from  it.  The  same  was 
also  the  case  with  Kepler's  Laws,  when  they  were  proved 

«  See  pp.  145,  146,  157,  158. 


252   RELATION  OF  INDUCTION  TO  DEDUCTION, 

deductively  from  the  theorem  of  the  Central  Force.  This 
mode  of  Verification  is  recommended  by  Mr.  Mill,  under 
the  name  of  the  Inverse  Deductive  or  Historical  Method, 
as  specially  applicable  to  generalisations  on  society  which 
have  been  inferred  inductively  from  the  study  of  history 
or  the  observation  of  mankind.  These  generalisations 
are  subsequently  verified  by  being  connected  deductively 
with  the  general  laws  of  mind  or  conduct  which  are  fur- 
nished by  the  study  of  Psychology  or  Ethology  \  It  is 
thus  shown  that  the  generalisations  of  history  are  such  as 
we  might  have  anticipated  a  priori  from  a  general  know- 
ledge of  human  nature,  and  each  branch  of  the  enquiry 
is  made  in  this  manner  to  afford  a  striking  confirmation 
of  the  results  arrived  at  by  the  other. 

It  frequently  happens  that  what  may  be  called  a  re- 
sidual phenomenon  affords  an  unexpected,  and,  on  that 
account,  a  striking  verification  of  some  law  which  is  not 
immediately  the  object  of  investigation.  Thus,  to  recur 
to  an  instance  already  adduced  for  another  purpose, 
when  it  was  found  that  the  difference  between  the  ob- 
served and  calculated  velocities  of  sound  was   exactly 

'  See  above,  pp.  204-207,  and  Mill's  Logic,  Bk.  VI.  ch.  x.  I 
cannot  agree  with  Mr.  Mill  in  attaching  any  special  importance  to 
the  order  in  which  the  respective  Methods  are  used  in  this  enquiry. 
Though  the  inductive  investigation,  based  on  the  facts  of  history  or 
observation,  generally  precedes  the  deductive  verification  from  the 
laws  of  psychology,  we  may,  and  sometimes  do,  begin  with  psycho- 
logical generalisations,  and  subsequently  verify  them  by  an  appeal 
to  observed  facts.  The  only  essential  point  is  that  the  two  Methods 
should  be  combined,  so  that  the  results  arrived  at  by  the  one  may 
corroborate  the  results  arrived  at  by  the  other. 


AND    VERIFICATION 


'^:>?^ 


accounted  for  by  the  law  of  the  development  of  heat  by 
compression,  this  law  acquired  so  novel  and  striking  a 
confirmation  as  to  leave  no  doubt  of  its  truth  or  univer- 
sality. 

It  need  hardly  be  remarked  that  any.  verification  of 
one  inductive  proof  by  another,  or  of  an  induction  by 
a  deduction,  or  of  a  deduction  by  an  induction,  should 
conform  with  the  laws  of  deductive  or  inductive  reasoning 
as  the  case  may  be.  Verification  is  not  a  distinct  mode 
of  proof,  but  is  simply  a  confirmation  of  one  proof  by 
another,  sometimes  of  a  deduction  by  an  induction, 
sometimes  of  an  induction  by  a  deduction,  and,  finally, 
sometimes  of  one  induction  or  deduction  by  another. 
It  must  also  be  borne  in  mind  that  the  term  is  not  in- 
frequently employed  to  designate  simply  the  confirma- 
tion of  a  hypothesis  by  an  appeal  to  facts. 

The  student  will,  of  course,  understand  that  it  is  not 
always  necessary  to  employ  Verification.  A  proof  may 
be  so  cogent  as  to  need  no  confirmation.  It  would  be 
absurd,  for  instance,  to  appeal  to  actual  measurement 
as  a  verification  of  the  proposition  enunciated  in  Euclid^ 
i.  47. 


CHAPTER  VI. 
On  the  Fallacies  incident  to  Induction. 

THE  errors  incidental  to  inductive  reasoning  and  to 
its  various  subsidiary  processes  have  already,  to  a  great 
extent,  been  noticed  in  the  preceding  chapters.  In 
laying  down  the  conditions  essential  to  the  correct 
conduct  of  a  process,  the  mistakes  which  result  from 
its  incorrect  conduct  necessarily  form  part  of  our  enquiry. 
Though,  therefore,  it  may  be  convenient  to  pass  the 
inductive  fallacies  in  review,  it  is  assumed  that  the  student 
is  already  acquainted  with  the  principal  errors  to  which 
his  processes  and  methods  are  liable. 

A.  To  begin  with  the  subsidiary  processes,  the  errors 
incident  to  the  process  of  observation,  or  '  the  fallacies 
of  mis-observation,'  are  well  classified  by  Mr.  Mill  as 
those  which  arise  from  Non-observation  and  those  which 
arise  from  Mal-observation. 

I.  Non-observation  may  consist  either  (i)  in  neglecting 
some  of  the  instances,  or  (2)  in  neglecting  some  of  the 
circumstances  attendant  on  a  given  instance. 

(i)  With  respect  to  the  non-observation  of  instances,  it 


FALLACIES  INCIDENT  TO  INDUCTION,      1$^ 

was  long  ago  pointed  out  by  Bacon  ^  that  there  is  in  the 
human  mind  a  peculiar  tendency  to  dwell  on  affirmative 
and  to  overlook  negative  instances.  Familiar  examples 
of  this  tendency  will  readily  occur  to  every  one.  We 
think  it  a  *  curious  coincidence '  that  we  should  suddenly 
meet  a  man  of  whom  we  have  just  been  talking,  that 
some  event  should  happen  of  which  we  dreamed  the  night 
before,  or  that  the  predictions  of  a  fortune-teller  or  an 
almanac  should  be  verified  by  the  facts.  The  explana- 
tion of  these  *  curious  coincidences'  is  that  our  at- 
tention is  arrested  by  the  affirmative  instances,  whereas 

*  *  Intellectus  humanus  in  iis  quoe  semel  placuerunt  (aut  quia 
recepta  sunt  et  credita,  aut  quia  delectant)  alia  etiam  omnia  trahit 
ad  suffragationem  et  consensum  cum  illis  :  et  licet  major  sit  instanti- 
arum  vis  et  copia,  quoe  occurrunt  in  contrarium ;  tamen  eas  aut  non 
observat,  aut  contemnit,  aut  distinguendo  summovet  et  rejicit,  non 
sine  magno  et  pernicioso  prejudicio,  quo  prioribus  illis  syllepsibus 
auctoritas  maneat  inviolata.  Itaque  recte  respondit  ille,  qui,  cum 
suspensa  tabula  in  templo  ei  monstraretur  eorum  qui  vota  solverant 
quod  naufragii  periculo  elapsi  sint,  atque  interrogando  premeretur, 
anne  turn  quidem  Deorum  numen  agnosceret,  quaesivit  denuo,  "  At 
ubi  sunt  illi  depicti  qui  post  vota  nuncupata  perierint  ? "  Eadem 
ratio  est  fere  omnis  superstitionis,  ut  in  astrologicis,  in  somniis,  omini- 
bus,  nemesibus,  et  hujusmodi ;  in  quibus  homines  delectati  hujusmodi 
vanitatibus  advertunt  eventus,  ubi  implentur ;  ast  ubi  fallunt,  licet 
multo  frequentius,  tamen  negligunt  et  praetereunt.  At  longe  subtil ius 
serpit  hoc  malum  in  philosophiis  et  scientiis ;  in  quibus  quod  semel 
placuit  reliqua  (licet  multo  firmiora  et  potiora)  inticit,  et  in  ordinem 
redigit.  Quinetiam  licet  abfuerit  ea,  quam  diximus,  delectatio  et 
vanitas,  is  tamen  humano  intellectui  error  est  proprius  et  perpetuus, 
ut  magis  moveatur  et  excitetur  affirmativis,  quam  negativis ;  cum 
rite  et  ordine  sequum  se  utrique  praebere  debeat :  quin  contra,  in 
omni  axiomate  vero  constituendo,  major  est  vis  instantioe  negativse.' 
— Novum  Organum,  Lib.  I.  Aph.  xlvi. 


256 


FALLACIES  INCIDENT 


the  numberless  instances  in  which  there  is  no  corre- 
spondence between  the  one  set  of  facts  and  the  other 
altogether  escape  our  notice.  We  probably  talk  scores 
of  times  during  the  day  of  persons  whom  we  do  not 
meet  immediately  afterwards ;  we  frequently  dream  in 
the  most  circumstantial  manner  of  events  which  never 
occur ;  and,  where  one  prediction  of  a  fortune-teller  is 
verified,  scores  are  probably  falsified.  The  weather-pro- 
phets of  the  almanacs  possess  a  considerable  advantage 
in  the  fact  that,  whereas,  at  all  times,  there  is  at  least  a 
considerable  chance  of  their  predictions  turning  out  true, 
there  are  certain  periods,  such  as  the  equinoxes,  at  which 
particular  kinds  of  weather  may  be  anticipated  with  a 
probability  amounting  almost  to  certainty. 

In  former  generations  *  coincidences '  of  this  kind  were 
regarded  not  simply  as  '  curious '  and  '  remarkable,'  but 
as  proofs  of  some  causal  connexion  between  the  events. 
To  talk  of  a  person  was  supposed  to  render  his  presence 
more  likely ;  a  verified  prediction  was  regarded  as  evi- 
dence of  second-sight ;  and  a  comet  which  was  observed 
to  be  followed  by  a  war  was  supposed  to  be,  if  not 
the  cause  of  the  war,  at  least  a  messenger  sent  from 
Heaven  to  proclaim  its  approach.  The  tendency  to  take 
note  of  affirmative,  and  to  overlook  negative  instances, 
is  one  of  the  causes  of  that  hasty  generalisation  of  which 
I  shall  speak  in  a  subsequent  part  of  this  chapter^ 

"  The  following  remarks  of  Sir  John  Herschel,  in  speaking  of  the 
verification  of '  signs  of  the  weather/  are  to  apposite,  that  1  append 
them  in  a  note  : — 


TO  INDUCTION, 


'2' 57 


This  tendency  is  considerably  intensified,  if  the  af- 
firmative instances  are  regarded  as  illustrations  of  some 
preconceived  theory^,  or  if  the  evidence  afforded  by 
them  be  supplemented  by  some  powerful  affection  of 
the  mind*.  It  seldom  happens  that  men  can  hold 
themselves  entirely  indifferent  with  respect  to  two  rival 

*  We  would  strongly  recommend  any  of  our  readers  whose  occu- 
pations lead  them  to  attend  to  the  "  signs  of  the  weather,"  and  who, 
from  hearing  a  particular  weather  adage  often  repeated,  and  from 
noticing  themselves  a  few  remarkable  instances  of  its  verification, 
have  "  begun  to  put  faith  in  it,"  to  commence  keeping  a  note-book, 
and  to  set  down  without  bias  all  the  instances  which  occur  to  them 
of  the  recognised  antecedent,  and  the  occurrence  or  non-occurrence 
of  the  expected  consequent,  not  omitting  also  to  set  down  the  cases 
in  which  it  is  left  undecided  ;  and,  after  so  collecting  a  considerable 
number  of  instances  Cnot  less  than  a  hundred \  proceed  to  form  his 
judgment  on  a  fair  comparison  of  the  favourable,  the  unfavourable, 
and  the  undecided  cases;  remembering  always  that  the  absence  of  a 
majority  one  way  or  the  other  would  he  in  itself  an  iniprohahility^ 
and  that,  therefore,  to  have  any  weight,  the  majority  should  be  a 
very  decided  one.  and  that  not  only  in  itself,  but  in  reference  to  the 
neutral  instances.  We  are  all  involuntarily  much  more  strongly  im- 
pressed by  the  fulfilment  than  by  the  failure  of  a  prediction,  and  it 
is  only,  when  thus  placing  ourselves  face  to  face  with  fact  and  ex- 
perience, that  we  can  fully  divest  ourselves  of  this  bias.' — Familiar 
Lectures  on  Scientific  Subjects,  Lecture  IV. 

^  *  Habet  enim  unusquisque  (praeter  aberrationes  naturae  humanae 
in  gencre)  specum  sive  cavcrnam  quandam  individuam,  quae  lumen 

naturae  frangit  et  corrumpit; vel  propter  differcntias  impres- 

sionum,  prout  occurrunt  in  animo  praeoccupato  et  praedisposito,  aut  in 
animo  aequo  et  sedato.' — Bacon's  Novum  Organum,  Lib.  I.  Aph.  xlii. 

*  *  Intellectus  humanus  luminis  sicci  non  est ;  sed  recipit  infusionem 
a  voluntate  et  affectibus ;  id  quod  generat  ad  quod  vult  scicntias : 
quod  enim  mavult  homo  verum  esse,  id  potius  credit.' — Novum  Or- 
ganum, Lib.  L  Aph.  xlix. 


258 


FALLACIES  INCIDENT 


opinions    and   apply   themselves   to   the   comparatively 
unexciting   task   of  collecting   evidence   impartially  on 
either  side.    To  avoid  taking  a  side  on  imperfect  informa- 
tion, even  where  our  interests  or  passions  are  not  directly 
concerned,  is  one  of  the  last  and  most  difficult  lessons 
learned  by  the  scientific  intellect,  and  by  ordinary  men 
it  is  regarded  as  a  sign  of  a  peculiarly  frigid  temper- 
ament, if  not  of  an  indifference  to  truth.     Thus,  when 
the  theory  involved  in  the  idea  of  witchcraft  had  once 
been  conceived  and  accepted,  and  especially  when  it 
had  led  to  the  invention  of  a  new  crime,  it  came  to 
be  held  that  the  burden  of  proof  lay  with  those  who 
called  its  reality  in  question.     Every  story  which   con- 
firmed  the    theory   would   be   greedily  received,    while 
instances  in  which  the  supposed  powers  of  the  witch 
had  failed,   if  noticed   at   all,   would   either   leave   but 
a    slight    impression    on    the    mind,   or   be   easily   ac- 
counted for  by  supposing  the  intervention  of  a  higher 
power.     To   the    numerous   class    engaged    in    the   ad- 
ministration   of  the    laws,   a   not   unnatural   reluctance 
to  question  the  justice  of  the  principles  on  which  they 
and  their  predecessors  had  been   in   the  habit   of  act- 
ing would   furnish   an   additional   inducement   to   pass 
lightly    over    negative    instances.      Fear,    or    dread    of 
eccentricity,    would    operate    in    the    case    of    others; 
and  thus  a  theory  of  the  most  preposterous  character, 
which,  to  a  mind  not  preoccupied,  received  little  or  no 
confirmation  from  facts'',  and  the  truth  of  which  could 
*  When  a  person  was  convinced  that  he  was  subject  to  the  evil 


TO  INDUCTION, 


259 


easily  have  been  brought  to  the  test,  maintained  its 
ground,  and  throughout  many  centuries  continued  to  pro- 
duce the  most  mischievous  results.  The  extent  of  the 
bias  to  which  the  mind,  in  its  observation  of  instances,  is 
exposed  from  the  influence  of  strong  affections,  is  patent 
to  every  one.  A  man  of  a  desponding  temperament  will 
dwell  on  the  number  of  those  who  have  failed,  a  man  of 
a  sanguine  temperament  on  the  number  of  those  who  have 
succeeded,  in  their  respective  professions.  A  man  with 
strong  sympathies  will  see  only  virtues  or  good  traits  of 
character,  where  one  of  a  malevolent  or  critical  dispo- 
sition will  see  only  vices  or  blemishes.  An  ardent  ad- 
herent of  a  religious  sect  or  a  political  party  will  see 
nothing  but  good  in  those  who  agree  with  him,  nothing 
but  evil  in  those  who  adopt  a  different  creed  or  profess 
to  be  guided  by  different  principles  of  policy. 

Many  of  the  above  errors  might  be  otherwise  described 
as  arising  from  the  confusion  between  absolute  and  relative 
frequency.  We  notice  how  often  an  event  occurs,  but  we 
do  not  notice  how  much  oftener  it  does  not  occur. 

Not  only  will  a  preconceived  opinion  or  a  powerful 
affection  come  in  aid  of  the  natural  tendency  of  men  to 
dwell  on  affirmative  and  overlook  negative  instances,  but 
they  will  often  cause  them  to  adhere  to  theories  for  which, 
whatever  may  have  been  the  history  of  their  formation, 


practices  of  a  witch,  this  conviction  would,  of  course,  sometimes 
produce  the  ill  effects  attributed  to  witchcraft  itself.  In  other  cases, 
some  event,  such  as  a  death  or  an  illness,  which  occurred  in  the 
ordinary  course  of  nature,  would  confirm  the  suspicion. 

S  2 


26o 


FALLACIES  INCIDENT 


there  is  absolutely  no  support  whatever  in  fact.     Thus, 
the  theory  which  prevailed  down  to  the  time  of  Galileo «, 
that  bodies  fall  to  the  earth  in  limes  inversely  propor- 
tional  to  their  weights,  so  that  a  body  weighing,  say, 
five  pounds,  would  fldl  in  a  time  five  times  as  short  as 
a  body  weighing  one  pound,  rested  on  absolutely  no 
evidence  except  the  fact  that,  in  consequence  of  the  re- 
sistance of  the  air,  the  heavier  body,  especially  if  it  be 
of  a  denser  material,  reaches  the  ground  in  a  shorter 
time  than  the  lighter  one;    still,  till  Galileo  made  his 
experiments,  at  the  end  of  the  sixteenth  century,  from 
the  leaning  tower  of  Pisa,  no  one  thought  of  bringing  to 
a  decisive  test  a  theory  which  it  was  so  easy  to  prove  or 
disprove.     Even,  without  having  recourse  to  experiment, 
one  would  have  imagined  that  the  most  casual  observa- 
tions of  falling  bodies  would  have  revealed,  to  a  mind 
not  strongly  pre-occupied,  the  strange  inaccuracy  of  this 
theory.     The  recei)tion  accorded  to  the  theory  that  the 
weight  of  the  elements  increases  in  a  tenfold  ratio,  so 
that  earth   is  ten  times  heavier  than  water,  water  ten 
times  heavier  than  air,  and  air  ten  times  heavier  than 
fire,  seems  still  more  astounding". 

In  Sir  Thomas  Browne's  Enquiries  into  Vulgar  and 
Common  Errors*,  we  have  an  examination  of  the  propo- 

«  Galilai  Systcma  Cosmicum,  Dial.  II. 

'  This  theory  appears  tt»  have  originated  in  a  mistaken  interpreta- 
tion of  a  passai^e  in  Aristotle,  De  Generatione  et  Corruftione,  II.  6. 
See  my  note  on  Bacon's  Novum  Organum,  Lib.  1.  Aph.  xlv. 

>■  13k.  IV.  ch.  vii. 


TO  I  ADDUCTION. 


2^1 


sition  that  *  men  weigh  heavier  dead  than  alive,  and  before 
meat  than  after.'  Here  are  two  extraordinary  paradoxes 
which  it  was  perfectly  easy  for  any  one  to  bring  to  a 
decisive  test ;  and  still,  though  an  appeal  to  facts  would 
at  once  have  been  fatal  to  them,  they  appear  to  have  met 
with  a  very  general  reception.  The  grounds  assigned 
for  the  prevalence  of  the  latter  opinion  are  so  curious 
that  they  deserve  to  be  transcribed.  *  Many  are  also  of 
opinion,  and  some  learned  men  maintain,  that  men  are 
lighter  after  meals  than  before,  and  that  by  a  supply 
and  addition  of  spirits  obscuring  the  gross  ponderosity 
of  the  aliment  ingested  ;  but  the  contrary  hereof  we  have 
found  in  the  trial  of  sundry  persons  in  different  sex  and 
ages.  And  we  conceive  men  may  mistake,  if  they  dis- 
tinguish not  the  sense  of  levity  unto  themselves,  and  in 
regard  of  the  scale,  or  decision  of  trutination.  For  after 
a  draught  of  wine,  a  man  may  seem  lighter  in  himself 
from  sudden  refection,  although  he  be  heavier  in  the 
balance,  from  a  corporal  and  ponderous  addition  ;  but 
a  man  in  the  morning  is  lighter  in  the  scale,  because 
in  sleep  some  pounds  have  perspired ;  and  is  also  lighter 
unto  himself,  because  he  is  refected.'  It  will  be  noticed 
that  'spirits'  are  supposed  to  possess  the  property  of 
positive  levity,  and  that,  consequently,  they  are  regarded 
as  making  any  body  into  which  they  enter  lighter  than 
it  was  before.  The  theory  that  certain  bodies  are 
positively  light  is  itself  an  instance  of  a  fallacy  of 
non-observation,  but,  as  will  be  seen  presently,  of  non- 
observation  of  circumstances  not  of  instances. 


262 


FALLACIES  INCIDENT 


Another  extraordinary  instance  of  a  statement  which 
obtained  acceptance  without  any  foundation  whatever  in 
fact  is  noticed  in  an  article  in  the  Quarterly  Review  for 
January,  1865,  on  '  Aristotle's  History  of  Animals.'  Here, 
however,  there  appears  to  be  no  assignable  reason  for  the 
mistake. 

*  Aristotle  held  some  peculiar  notions  with  respect  to  the 
skull.     He  says,  "  that  part  of  the  head  which  is  covered  with 
hair  is  called  the  cranium  ;  the  fore  part  of  this  is  called  the 
sinciput ;    this  is  the  last  formed,  being  the  last  part  in  the 
body  which  becomes  hard."     He  correctly  alludes  here  to  the 
opening  in  the  frontal  bone  of  a  young  infant,  which  gradually 
becomes  hardened  by  ossification  ;  "  the  hinder  part  is  the 
occiput,  and  between  the  occiput  and  sinciput  is  the  crown 
of  the  head  :  the  brain  is  placed  beneath  the  sinciput,  and 
the  occiput  is  empty  (!).     The  skull  has  sutures  :  in  women 
there  is  but  one  placed  in  a  circle  (!)  ;  men  have  generally 
three  joined  in  one,  and  a  man's  skull  has  been  seen  without 
any  sutures  at  all."     The  often  repeated  question  as  to  how 
far  Aristotle's  observations  are  the  result  of  his  own  investi- 
gation, naturally  suggests  itself  again  here  ;    had  Aristotle 
ever  dissected  a  human  body,  he  never  would  have  asserted 
a  proposition  so  manifestly  false  as  that  the  back  of  the  head 
is   empty,  or  that   women  have  one  only  suture  placed  in 
a  circle.' 

The  passage  here  noticed  occurs  in  the  Historia  Ani- 
malium,  Bk.  I.  ch.  vii.     Cp.  Bk.  HI.  ch.  vii. 

A  still  more  remarkable  instance  of  this  description  of 
fallacy  is  noticed  in  Mr.  Lecky's  History  of  European 
Morals  from  Augustus  to  Charkinagne  ^ 

•  Vol.  i.  p.  394- 


TO  INDUCTION, 


^<^3 


'Aristotle,  the  greatest  naturalist  of  Greece,  had  observed 
that  it  was  a  curious  fact,  that  on  the  sea-shore  no  animal 
ever  dies  except  during  the  ebbing  of  the  tide.  Several  cen- 
turies later,  Pliny,  the  greatest  naturalist  of  an  empire  that 
was  washed  by  many  tidal  seas,  directed  his  attention  to  this 
statement.  He  declared  that,  after  careful  observations  which 
had  been  made  in  Gaul,  it  had  been  found  to  be  inaccurate, 
for  what  Aristotle  stated  of  all  animals,  was  in  fact  only  true 
of  man.  It  was  in  1727  and  the  two  following  years,  that 
scientific  observations  made  at  Rochefortand  at  Brest  finally 
dissipated  the  delusion.' 

I  add  one  more  instance,  showing  the  extraordinary 
readiness  with  which  men,  even  of  remarkable  acuteness 
and  erudition,  will  accept  the  strangest  fancies,  though 
absolutely  unsupported  by  evidence.  It  is  taken  from 
Glanvill's  Scepsis  Scietitifica,  published  in  1665  ^V— 

*  Besides  this  there  is  another  way  of  secret  conveyance 
that's  whisper'd  about  the  World,  the  truth  of  which  I  vouch 
not,  but  the  possibility :  it  is  conference  at  distance  by  sym- 
pathized handes.  For  say  the  relatours  of  this  strange  secret  : 
The  hands  of  two  friencis  being  allyed  by  the  transferring  of 
Flesh  from  one  into  the  other,  and  the  place  of  the  Letters 
mutually  agreed  on  ;  the  least  prick  in  the  hand  of  one,  the 
other  will  be  sensible  of,  and  that  in  the  same  part  of  his  own. 
And  thus  the  distant  friend,  by  a  new  kind  of  Chiromancy, 
may  read  in  his  own  hand  what  his  correspondent  had  set 
down  in  his.  For  instance,  would  I  in  London  acquaint  my 
intimate  in  Paris,  that  I  am  well :  I  would  then  prick  that 
part  where  I  had  appointed  the  letter  [I]  and,  doing  so  in 
another  place  to  signifie  that  word  was  done,  proceed  to  [A], 

"  Scepsis  Scientifca,  ch.  24. 


264 


FALLACIES  INCIDENT 


thence  to  [M],  and  so  on,  till  I  had  finisht  what  I  intended 
to  make  known.' 

The  influence  of  some  strong  passion  or  affection  in 
causing  men  to  accept  theories  without  any  support  from 
observation  or  experiment,  and  often  in  direct  defiance 
of  them,  may  be  illustrated  from  almost  all   the   more 
powerful  feelings  of  human  nature.     The  mythologies  of 
every  nation  are  full  of  the  wildest  and  most  improbable 
stories,  originating  partly  in  the  strength  of  the  religious 
sentiment,  partly  in  that  love  of  the  marvellous  which 
seems  to  be  connatural  to  every  race  of  mankind,  partly 
in  later  misinterpretations  of  that  poetical   language  in 
which  early  races  are  wont  to  clothe  their  ideas.     Thus, 
stories   of  the   transformation   of  men    into  beasts,  of 
rivers  flowing  backwards,  of  images  falling  down  from 
heaven,  besides  other  tales  still  more  fantastic,  have  been 
greedily  received  by  generation  after  generation,  in  spite 
of  all  the  analogies  of  nature  and  without   one   single 
instance  to  confirm  them.     The  beliefs  in  ghosts,  spirit- 
rapping,    and  similar  phenomena,  seem    to   have   their 
origin    in    man's    insatiable  craving  for  the  marvellous, 
acting   often  in  combination  with  the  feelings  of  fear, 
hope,  or  curiosity.     One  of  the    most  powerful  agents 
in  human  affairs  is  the  passion  of  avarice  or  the  insa- 
tiable  desire   for   the  accumulation  of  wealth.     In  the 
middle  ages,  this  passion  led  the  alchemists,  contrary  to 
all  experience,  to  the  belief  that  it  was  open  to  men  to 
become  suddenly  and  enormously  rich  by  discovering  the 
secret  of  transmuting  other  metals  into  gold.     In  modern 


TO  INDUCTION, 


26^ 


times  it  has  frequently  led,  and  still  leads,  men  to  embark 
in  the  most  desperate  speculations,  which  no  scientific 
calculation  of  chances  would  justify.  In  a  lottery,  for 
instance  (which  is  a  comparatively  innocuous  form  of 
speculation),  the  value  of  the  chance  is,  owing  to  the 
expenses  of  management  and  the  profit  required  by  the 
projectors,  invariably  much  less  than  the  price  paid  for 
the  ticket.  But,  perhaps,  the  most  remarkable  exempli- 
fication of  the  unreasoning  desire  for  sudden  accessions 
of  wealth  is  to  be  found  in  the  pertinacity  with  which, 
in  spite  of  every  warning,  men  would,  till  within  quite 
a  recent  period,  expend  large  fortunes  in  sinking  shafts 
for  coal  and  other  minerals  in  strata  in  which  the  uni- 
versal experience  of  geologists  and  miners  testified  against 
their  occurrence.  In  this,  as  in  many  other  cases,  the 
observations  of  competent  authorities  went  for  nothing ; 
the  passion  was  so  absorbing  that  it  alone  determined 
action. 

The  fallacies  due  to  non-observation  of  instances  may 
be  further  exemplified  by  the  tendency  of  the  mind  to 
acquiesce  in  the  first  instances  which  offer  themselves  ", 
especially  if  they  be  of  a  striking  kind  ^^,  instead  of  care- 


"  *  Axiomata,  quae  in  usu  sunt,  ex  tenui  et  manipulari  experientia, 
et  paucis  particularibus,  qua^  ut  plurimum  occurrunt,  fluxere  ;  et  sunt 
fere  ad  mensurani  eorum  facta  et  extensa.' — Novum  Organum,  Lib. 
I.  Aph.  XXV. 

'^  '  Intellectus  humanus  illis,  quae  simul  et  subito  mentem  ferire  et 
subire  possunt,maxime  movetur  ;  a  quibus  phantasia  impleri  et  inflari 
consuevit :  reliqua  vero  modo  quodani,  licet  imperceptibili,  ita  se 
habere  fingit  el  supponit,  quomodo  sc  Labent  pauca  ilia  quibus  mens 


266 


FALLACIES  INCIDENT 


fully  searching  for  other  instances  of  a  similar   nature 
with  which  to  compare  and  by  means  of  which  to  in- 
terpret them.      Thus,  the  phenomena  of  thunder  and 
lightning  would  probably  have  received  a  much  earlier 
explanation,  had  the  attention  of  men  been  sooner  di- 
rected to  the  instances  of  electricity  which  nature  presents 
of  a  less  striking  kind  and  on  a  smaller  scale.     Again,  the 
difficulties  presented  to  early  speculators  by  volcanoes 
and  earthquakes  would  have   been   considerably   dimi- 
nished, had   they  been  aware  of  the  fact  that  there  is 
hardly  any  portion  of  the  earth's  surface  which  is  not 
undergoing  a  constant  change  of  level  by  the   process 
either  of  elevation  or  of  subsidence,  though  such  change 
is  usually  imperceptible  to  each  single  generation.     The 
mistakes  originating  in  this  source  of  error  are  count- 
less.    We  observe  certain  peculiarities  in  some  particular 
representative  of  a  class,  profession,  or  nation,  and  then 
proceed   to   argue   as  if  all  the  members  of  the  class, 
profession,  or  nation  were  like  him.     Or,  a  person  on 
his  travels  in  some  country  is  unfavourably   impressed 
with  the  hotel-keepers,  porters,  and  carriage-drivers,  and 
then  proceeds  to  denounce  the  whole  nation  to  which 
they  belong,  as  if  the  characteristics  of  a  few  exceptional 
classes  were  the  characteristics  of  a  nationality  ^l 

obsidetur  ;  ad  ilium  vero  transcursum  ad  instantias  remotas  et  hetero- 
geneas,  per  quas  axiomata  tanciuam  igne  probantur,  tardus  omnino 
intellectus  est  et  inhabilis,  nisi  hoc  illi  per  duras  leges  et  violentum 
imperium  imponatur.'— i\w«w  Organum,  Lib.  I.  Aph.  xlvii. 

»3  The  history  of  the  French  language  furnishes  a  striking  instance 
of  non-observation  and  of  the  curious  and  baseless  theories  to  which 


TO   INDUCTION. 


267 


The  student  must  have  already  perceived  that  I  am 
trenching  on  Fallacies  of  Generalisation.  When  we 
proceed  to  treat  insufficient  evidence,  or  the  absence  of 
evidence,  or  popular  beliefs  which  run   counter  to  all 

it  may  lead :  *  It  is  well  known  that  before  certain  feminine  sub- 
stantives, such  as  messcy  nihe,  soif,  /aim,  peur,  &c.,  the  adjective 
^raw^  keeps  its  masculine  termination,  grand messe. grand: mhe,  «&c. 
Why  so  ?  Grammarians,  who  are  puzzled  by  nothing,  tell  us  without 
hesitation  that  grand  is  here  put  for  grande,  and  that  the  apostrophe 
marks  the  suppression  of  the  final  e.  But  the  good  sense  of  ever}' 
scholar  protests  against  this  :  after  having  learnt  in  childhood  that  e 
mute  is  cut  off  before  a  vowel,  and  never  before  a  consonant,  he  is 
told  that  the  e  is  here  cut  off  without  the  slightest  reason  in  such 
phrases  as  grand  route,  &c.  The  real  explanation  is  in  fact  a  very 
different  one.  In  its  beginning,  French  grammar  was  simply  the 
continuation  and  prolongation  of  Latin  grammar  ;  consequently  the 
Old  French  adjectives  followed  in  all  points  the  Latin  adjective; 
those  adjectives  which  had  two  terminations  for  masculine  and 
feminine  in  Latin  (as  bonus,  bona)  had  two  in  Old  French,  whereas 
those  Latin  adjectives  which  had  but  one  (as  grandis,fortts,  &c.) 
had  only  one  in  French.  In  the  thirteenth  century  men  said  une 
grand  femme,  grandis  femina ;  utie  dme  mortel,  anima  mortal  is  ; 
une  coutume  cruel,  consuetudo  crudelis ;  une  plaine  vert,  planities 
viridis,  &c.  In  the  fourteenth  century  the  meaning  of  this  distinction 
was  no  longer  understood  ;  and  men,  deeming  it  a  mere  irregularity, 
altered  the  form  of  the  second  to  that  of  the  first  class  of  adjectives, 
and  wrote  grande,  verte,  forte,  &c.,  after  the  pattern  of  bonne,  &c. 
A  trace  of  the  older  and  more  correct  form  survives  in  such  expres- 
sions as  grand'mere,  grand'route,  grand'faiin,  grand  garde,  &c., 
which  are  the  debris  of  the  older  language.  In  the  seventeenth 
century,  Vaugelas  and  the  grammarians  of  the  age,  in  their  ignorance 
of  the  historic  reason  of  this  usage,  pompously  decreed  that  the  form 
of  these  words  arose  from  an  euphonic  suppression  of  the  e  mute, 
which  must  be  indicated  by  an  apostrophe.' — Brachet's  Historical 
Grammar  of  the  French  Tongue,  Dr.  Kitchin's  Transl.,  Preface, 
p.  vi  ;  Seventh  Edition,  pp.  xxvi-vii. 


268 


FALLACIES  INCIDENT 


the  evidence  available,  as  if  they  afforded  perfectly  suf- 
ficient evidence,  the  fallacy  is  one  of  inference,  and,  if 
the  simulated  inference  be  inductive,  it  is  a  Fallacy  of 
Generalisation.     But  the  absence  or  insufficiency  of  the 
evidence,  if  due  to  our   not   having   kept   our   minds 
sufficiently  open  to  facts  or  not  having  taken  sufficient 
pains  to  collect  all  the  facts  pertinent  to  the  question, 
is  a  Fallacy  of  Non-observation,  and  is  a  defect  in  the 
preliminary  process  rather  than  in  the  inductive  infer- 
ence itself.    All  the  instances  described  above,  I  believe, 
fall  under  this  head,  though  the  inferences  founded  upon 
them,  where  they  possess  any  show  of  justification  at  all, 
are  cases  of  unwarranted  Inductio  per  Enumerationem 
Simplicem,  and   so   afford  illustrations  of  Fallacies  of 
Generalisation. 

(2)  The  second  division  of  the  Fallacies  of  Non-obser- 
vation is  the  fallacy  which  arises  from  overlooking  some 
of  the  material  circumstances  attendant  on  a  given  in- 
stance. Here  the  defect  is  not  in  the  number  or  per- 
tinency of  the  instances,  but  in  their  character;  the 
description  of  the  instances  themselves  is  untrustworthy. 
Till  we  have  ascertained  that  we  are  fully  acquainted  with 
all  the  material  circumstances  of  the  cases  examined,  we 
cannot  rely  upon  our  facts,  and,  consequently,  we  have 
no  right  to  proceed  to  ground  any  inference  upon  them. 
*The  circumstances,' says  Sir  John  Herschel^  'which 

»  Ilcrschel's    Discourse   on   the   Study  of  Natural  Philosophy. 
§  III. 


TO  INDUCTION, 


269 


accompany  any  observed  fact,  are  main  features  in  its 
observation,  at  least  until  it  is  ascertained  by  sufficient 
experience  what  circumstances  have  nothing  to  do  with 
it,  and  might  therefore  have  been  left  unobserved  without 
sacrificing  the  fact.  In  observing  and  recording  a  fact, 
therefore,  altogether  new,  we  ought  not  to  omit  any  cir- 
cumstance capable  of  being  noted,  lest  some  one  of  the 
omitted  circumstances  should  be  essentially  connected 
with  the  fact.  .  .  .  For  instance,  in  the  fall  of  meteoric 
stones,  flashes  of  fire  are  seen  proceeding  from  a  cloud, 
and  a  loud  rattling  noise  like  thunder  is  heard.  These 
circumstances,  and  the  sudden  stroke  and  destruction 
ensuing,  long  caused  them  to  be  confounded  with  an 
effect  of  lightning,  and  called  thunderbolts.  But  one 
circumstance  is  enough  to  mark  the  difference :  the  flash 
and  sound  have  been  perceived  occasionally  to  emanate 
from  a  very  small  cloud  insulated  in  a  clear  sky  ;  a  com- 
bination of  circumstances  which  never  happens  in  a 
thunder  storm,  but  which  is  undoubtedly  intimately  con- 
nected with  their  real  origin.' 

The  extreme  difficulty  of  obtaining,  by  means  of  the 
thermometer,  a  correct  measure  of  the  temperature  of 
the  atmosphere,  owing  to  the  conduction  of  heat  by  the 
stand  and  its  radiation  from  surrounding  objects,  and  the 
consequent  errors  frequently  made  by  observers  from  not 
sufficiently  providing  against,  or  allowing  for,  these 
sources  of  interference,  will  serve  to  every  one  as  a 
familiar  illustration  of  the  great  importance  of  the  caution 
which  it  is  here  intended  to  furnish. 


268 


FALLACIES  INCIDENT 


the  evidence  available,  as  if  they  afforded  perfectly  suf- 
ficient evidence,  the  fallacy  is  one  of  inference,  and,  if 
the  simulated  inference  be  inductive,  it  is  a  Fallacy  of 
Generalisation.     But  the  absence  or  insufficiency  of  the 
evidence,  if  due  to  our   not   having   kept   our   minds 
sufficiently  open  to  facts  or  not  having  taken  sufficient 
pains  to  collect  all  the  facts  pertinent  to  the  question, 
is  a  Fallacy  of  Non-observation,  and  is  a  defect  in  the 
preliminary  process  rather  than  in  the  inductive  infer- 
ence itself.    All  the  instances  described  above,  I  believe, 
fall  under  this  head,  though  the  inferences  founded  upon 
them,  where  they  possess  any  show  of  justification  at  all, 
are  cLses  of  unwarranted  Inductio  per  Enumerationem 
Simplicem,  and   so   afford  illustrations  of  Fallacies  of 
Generalisation. 

(2)  The  second  division  of  the  Fallacies  of  Non-obser- 
vation is  the  fallacy  which  arises  from  overlooking  some 
of  the  material  circumstances  attendant  on  a  given  in- 
stance. Here  the  defect  is  not  in  the  number  or  per- 
tinency of  the  instances,  but  in  their  character;  the 
description  of  the  instances  themselves  is  untrustworthy. 
Till  we  have  ascertained  that  we  are  fully  acquainted  with 
all  the  material  circumstances  of  the  cases  examined,  we 
cannot  rely  upon  our  facts,  and,  consequently,  we  have 
no  right  to  proceed  to  ground  any  inference  upon  them. 
*The  circumstances,' says  Sir  John  Herscher\  'which 

»♦  Ilcrschers    Discourse   on   the  Study  of  Natural  Philosophy, 
§  III. 


TO  INDUCTION. 


269 


accompany  any  observed  fact,  are  main  features  in  its 
observation,  at  least  until  it  is  ascertained  by  sufficient 
experience  what  circumstances  have  nothing  to  do  with 
it,  and  might  therefore  have  been  left  unobserved  without 
sacrificing  the  fact.  In  observing  and  recording  a  fact, 
therefore,  altogether  new,  we  ought  not  to  omit  any  cir- 
cumstance capable  of  being  noted,  lest  some  one  of  the 
omitted  circumstances  should  be  essentially  connected 
with  the  fact.  .  .  .  For  instance,  in  the  fall  of  meteoric 
stones,  flashes  of  fire  are  seen  proceeding  from  a  cloud, 
and  a  loud  rattling  noise  like  thunder  is  heard.  These 
circumstances,  and  the  sudden  stroke  and  destruction 
ensuing,  long  caused  them  to  be  confounded  with  an 
effect  of  lightning,  and  called  thunderbolts.  But  one 
circumstance  is  enough  to  mark  the  difference :  the  flash 
and  sound  have  been  perceived  occasionally  to  emanate 
from  a  very  small  cloud  insulated  in  a  clear  sky  ;  a  com- 
bination of  circumstances  which  never  happens  in  a 
thunder  storm,  but  which  is  undoubtedly  intimately  con- 
nected with  their  real  origin.' 

The  extreme  difficulty  of  obtaining,  by  means  of  the 
thermometer,  a  correct  measure  of  the  temperature  of 
the  atmosphere,  owing  to  the  conduction  of  heat  by  the 
stand  and  its  radiation  from  surrounding  objects,  and  the 
consequent  errors  frequently  made  by  observers  from  not 
sufficiently  providing  against,  or  allowing  for,  these 
sources  of  interference,  will  serve  to  every  one  as  a 
familiar  illustration  of  the  great  importance  of  the  caution 
which  it  is  here  intended  to  furnish. 


15 


270  FALLACIES  INCIDENT 

The  following  examples,  adduced  by  Mr.  Mill  -,  are 
so  interesting  and  appropriate,  that  I  take  the  liberty 
of  transcribing  them  : — 

*Such   for  instance  [namely,  the  imperfect  observation  of 
particular  facts],  was  one  of  the  mistakes  committed  in  the 
celebrated  phlogistic  theory ;  a  doctrine  which  accounted  for 
combustion  by  the  extrication  of  a  substance  called  phlogiston, 
supposed  to  be  contained  in  all  combustible   matter.     The 
hypothesis  accorded  tolerably  well  with  superficial  appear- 
ances •  the  ascent  of  flame  naturally  suggests  the  escape  of 
a  substance  ;  and  the  visible  residuum  of  ashes,  in  bulk  and 
weight,  generally  falls  extremely  short  of  the  combustible 
material      The  error  was  non-observation  of  an  important 
portion  of  the  actual  residue,  namely,  the  gaseous  products 
of  combustion.     When  these  were  at  last  noticed  and  brought 
into   account,  it  appeared    to  be  an   universal  law  that  all 
substances  gain  instead  of  losing  weight  by  undergoing  com- 
bustion ;  and,  after  the  usual  attempt  to  accommodate  the 
old  theory  to  the  new  fact  by  means  of  an  arbitrary  hypo- 
thesis  (that    phlogiston   had  the  quality  of  positive  levity 
instead  of  gravity),  chemists   were  conducted   to  the  true 
explanation,  namely,  that,  instead  of  a  substance  separated, 
there  was  on  the  contrary  a  substance  absorbed. 

*  Many  of  the  absurd  practices  which  have  been  deemed 
to  possess  medicinal  efficacy,  have  been  indebted  for  their 
reputation  to  non-observance  of  some  accompanying  circum- 
stance which  was  the  real  agent  in  the  cures  ascribed  to  them. 
Thus  of  the  sympathetic  powder  of  Sir  Kenelm  Digby  : 
''  Whenever  any  wound  had  been  inflicted,  this  powder  was 
applied  to  the  weapon  that  had  inflicted  it,  which  was,  more- 
over, covered  with  ointment,  and  dressed  two  or  three  times 
a  day.     The  wound  itself,  in  the  meantime,  was  directed  to 

15  System  of  Logic,  Bk.  V.  ch.  iv.  §  4. 


TO  INDUCTION 


271 


be  brought  together,  and  carefully  bound  up  with  clean  linen 
rags,  but,  above  all,  to  be  let  alone  for  seven  days,  at  the  end 
of  which  period  the  bandages  were  removed,  when  the 
wound  was  generally  found  perfectly  united.  The  triumph 
of  the  cure  was  decreed  to  the  mysterious  agency  of  the 
sympathetic  powder  which  had  been  so  assiduously  applied 
to  the  weapon,  whereas  it  is  hardly  necessary  to  observe  that 
the  promptness  of  the  cure  depended  upon  the  total  ex- 
clusion of  air  from  the  wound,  and  upon  the  sanative  opera- 
tions of  nature  not  having  received  any  disturbance  from  the 
officious  interference  of  art.  The  result,  beyond  all  doubt, 
furnished  the  first  hint  which  led  surgeons  to  the  improved 
practice  of  healing  wounds  by  what  is  technically  called  the 
first  intetition  '^" ' 

The  next  example  I  extract  from  Bp.  Wilkins'  very 
curious  tractate,  entitled  A  Discovery  of  a  New  World, 
or  a  Discourse  tending  to  prove  that  'tis  probable  there  may 
be  another  Habitable  World  in  the  Moon  : — 

*  He  [that  is, '  a  late  reverend  and  learned  Bishop,'  writing 
*  under  the  feigned  name  of  Domingo  Gonsales  '  ^']  supposeth 
that  there  is  a  natural  and  usual  passage  for  many  creatures 
betwixt  our  earth  and  this  planet.  Thus,  he  says,  those  great 
multitudes  of  locusts,  wherewith  divers  countries  have  been 
destroyed,  do  proceed  from  thence.  And  if  we  peruse  the 
authors  who  treat  of  them,  we  shall  find  that  many  times 
they  fly  in  numberless  troops  or  swarms,  and  for  sundry  days 
together  before  they  fall  are  seen  over  those  places  in  great 
high  clouds,  such  as,  coming  nearer,  are  of  extension  enough 

1*  Dr.  Taris'  Pharmacologia,  pp.  23-24. 

"  The  small  tract  here  referred  to  is  republished  in  vol.  viii.  of 
the  Harleian  Miscellanies  1  Park's  Edition) .  The  author  was  Francis 
Godwin,  afterwards  Bishop  of  Hereford,  and  author  of  the  well- 
known  book  De  Prcesulibus  Anglia  Commentarius. 


272 


FALLACIES  INCIDENT 


to  obscure  the  day,  and  hinder  the  light  of  the  sun.  From 
which,  together  with  divers  other  such  relations,  he  concludes 
that  'tis  not  altogether  improbable  they  should  proceed  from 
the  moon.  Thus ,  likewise ,  he  supposes  the  swallows,  cuckoos, 
nightingales,  with  divers  other  fowl,  which  are  with  us  only 
half  a  year,  to  fly  up  thither  when  they  go  from  us.  Amongst 
which  kind,  there  is  a  wild  swan  in  the  East  Indies,  which  at 
certain  seasons  of  the  year  do  constantly  take  their  flight 
thither.  Now,  this  bird  being  of  a  great  strength,  able  to 
continue  for  a  long  flight,  as  also  going  usually  in  flocks  like 
our  wild  geese,  he  supposeth  that  many  of  them  together 
might  be  thought  to  carry  tlie  weight  of  a  man  ;  especially  if 
an*engine  were  so  contrived  (as  bethinks  it  might)  that  each 
of  them  should  bear  an  equal  share  in  the  burden.  So  that, 
by  this  means,  'tis  easily  conceivable  how  once  a  year  a  man 
might  finish  such  a  voyage  ;  going  along  with  these  birds  at 
the  beginning  of  winter,  and  again  returning  with  them  in  the 
sprmg '  . 

A  more  accurate  and  extended  series  of  observations 
would,  of  course,  have  shown  that  the  birds  and  locusts 
migrated  from  other  parts  of  the  earth's  surface. 

It  is  not  necessary  to  multiply  examples  of  the  errors 
arising  from  slovenliness  and  inattention  in  the  collec- 
tion or  examination  of  our  instances.  The  necessity 
of  maintaining  the  strictest  caution  and  accuracy  in 
the  conduct  of  our  observations  and  experiments  has 
already  been  insisted  upon  in  the  Second  Chapter  of 
this  work. 

II.   Besides  the  errors  which  originate  in  the  neglect  of 
instances  or  of  some  of  the  circumstances  which  are  con- 
^'^  Wilkins  Discovery  of  a  New  World,  Fifth  Edition,  p.  i6o. 


TO  INDUCTION, 


273 


nected  with  a  given  instance,  there  is  another  class  of 
errors  derived  from  mistaking  for  observation  that  which 
is  not  observation  at  all,  but  inference.  To  this  class  of 
errors  Mr.  Mill  gives  the  name  of  Fallacies  of  Mal- 
Observation.  That  which  is  strictly  naatter  of  perception 
does  not  admit  of  being  called  in  question ;  it  is  the 
ultimate  basis  of  all  our  reasoning,  and,  if  we  are 
to  repose  any  confidence  whatever  in  the  exercise  of 
our  faculties,  must  be  taken  for  granted.  But  there  are 
few  of  our  perceptions,  even  of  those  which  to  the  un- 
philosophical  observer  appear  to  be  the  simplest,  which 
are  not  inextricably  blended  with  inference.  Thus,  as 
is  well  known  to  every  student  of  psychology,  in  what 
are  familiarly  called  the  visual  perceptions  of  distance  and 
of  form,  the  only  perception  proper  is  that  of  the  various 
tints  of  colour  acting  on  the  retina  of  the  eye,  and  it  is 
by  a  combination  of  this  with  perceptions  of  touch,  and 
of  the  muscular  sense,  that  the  mind  gains  its  power  of 
determining  form  and  distance.  Now,  a  judgment  of  this 
kind,  which  is  really  due  to  inference,  is,  especially  by 
the  uneducated  and  unreflecting,  perpetually  mistaken  for 
that  which  is  due  to  direct  observation  ;  and  thus  what  is 
really  only  an  inference  from  facts  is  often  emphatically 
asserted  to  be  itself  a  matter  of  fact.  '  In  proportion,' 
says  Mr.  Mill  ^\  '  to  any  person's  deficiency  of  knowledge 
and  mental  cultivation,  is  generally  his  inability  to  dis- 
criminate between  his  inferences  and  the  perceptions  on 
which  they  were  grounded.  Many  a  marvellous  tale, 
"  Mill's  Lo^ic,  Bk.  V.  ch.  iv.  §  5. 


274 


FALLACIES  INCIDENT 


many  a  scandalous  anecdote,  owes  its  origin  to  this  in- 
capacity.   The  narrator  relates,  not  what  he  saw  or  heard, 
but  the  impression  which  he  derived  from  what  he  saw  or 
heard,  and  of  which  perhaps  the  greater  part  consisted 
of  inference,  though  the  whole  is  related  not  as  inference 
but  as  matter-of-fact.      The   difficulty  of  inducing  wit- 
nesses to  restrain  within  any  moderate  limits  the  inter- 
mixture of  their  inferences  with  the  narrative  of  their 
perceptions,    is   well    known    to    experienced    cross-ex- 
aminers ;  and  still  more  is  this  the  case  when  ignorant 
persons  attempt  to  describe  any  natural  phenomenon. 
"  The  simplest  narrative,"  says  Dugald  Stewart,  "  of  the 
most  illiterate  observer  involves  more  or  less  of  hypo- 
thesis;  nay,  in  general,  it  will  be  found  that,  in   pro- 
portion to  his  ignorance,  the  greater  is  the  number  of 
conjectural  principles  involved    in    his  statements.      A 
village   apothecary  (and,  if  possible,   in  a  still   greater 
degree,  an  experienced  nurse)  is  seldom  able  to  describe 
the  plainest  case,  without   employing  a  phraseology  of 
which  every  word   is  a  theory  :    whereas  a  simple  and 
genuine  specification  of  the  phenomena  which  mark  a 
particular   disease;   a   specification   unsophisticated   by 
fancy,  or  by  preconceived  opinions,  may  be  regarded  as 
unequivocal  evidence  of  a  mind  trained  by  long  and 
successful  study  to  the  most  difficult  of  all  arts,  that  of 
the  faithful  interpretation  of  nature." ' 

No  better  instance  of  the  Fallacy  of  Mal-observation 
can  be  given  than  what  was  called  the  common-sense 
argument  against  the  truth  of  the  Copernican  System. 


TO  INDUCTION. 


'^75 


That  the  earth  should  move  round  the  sun,  men  said,  was 
impossible ;  for,  every  day,  they  saw  the  sun  rise  and  set 
and  perform  his  course  in  the  heavens.  They  felt  the 
earth  at  rest,  they  saw  the  sun  in  motion,  and  it  was 
absurd  to  call  upon  them  to  disbelieve  the  direct  evidence 
of  their  senses.  It  need  hardly  be  said  that  what  they 
mistook  for  the  direct  evidence  of  their  senses  was  really 
an  inference.  What  they  saw  was  consistent  with  one 
or  other  of  two  hypotheses,  that  the  sun  moved,  or  that 
the  earth  moved ;  and,  neglecting  to  take  any  account  of 
the  latter,  they  assumed  the  former.  If  it  were  not  for 
the  impressions  of  a  contrary  kind  derived  from  the 
actual  motion  of  the  carriage,  a  man,  whirled  along  in 
a  railway  train,  might  with  equal  justice  maintain,  by  an 
appeal  to  the  evidence  of  his  eyesight,  that  the  trees  and 
the  houses  were  running  past  him. 

Ventriloquism  supplies  another  familiar  instance  of  the 
same  error.  A  man  who  had  never  before  been  imposed 
upon  by  the  tricks  of  a  ventriloquist,  and  who  was  not 
aware  of  the  character  of  the  deception,  would  be  positive 
in  maintaining  that  he  had  the  direct  evidence  of  the 
sense  of  hearing  in  support  of  his  belief  that  the  sound 
he  heard  proceeded  from  a  particular  person  or  a  par- 
ticular part  of  the  building  other  than  that  from  which  it 
really  came.  The  fact,  of  course,  is  that  the  sound  itself  is 
all  that  is  directly  perceived  by  the  sense  of  hearing  ;  the 
reference  of  it  to  a  particular  person  or  a  particular  place 
is  an  act  of  inference  grounded  upon  constant,  or  at 
least  frequent,  association.     What  is  done  by  the  ven- 

T  2 


274 


FALLACIES  INCIDENT 


many  a  scandalous  anecdote,  owes  its  origin  to  this  in- 
capacity.    The  narrator  relates,  not  what  he  saw  or  heard, 
but  the  impression  which  he  derived  from  what  he  saw  or 
heard,  and  of  which  perhaps  the  greater  part  consisted 
of  inference,  though  the  whole  is  related  not  as  inference 
but  as  matter-of-fact.      The   difficulty  of  inducing  wit- 
nesses  to  restrain  within  any  moderate  limits  the  inter- 
mixture of  their  inferences  with  the  narrative  of  their 
perceptions,    is   well    known    to    experienced   cross-ex- 
aminers ;  and  still  more  is  this  the  case  when  ignorant 
persons  attempt  to  describe  any  natural  phenomenon. 
"  The  simplest  narrative,"  says  Dugald  Stewart,  "  of  the 
most  illiterate  observer  involves  more  or  less  of  hypo- 
thesis;   nay,  in  general,  it  will  be  found  that,  in    pro- 
portion to  his  ignorance,  the  greater  is  the  number  of 
conjectural  principles  involved    in   his  statements.      A 
village   apothecary  (and,  if  possible,   in  a  still   greater 
degree,  an  experienced  nurse)  is  seldom  able  to  describe 
the  plainest  case,  without   employing  a  phraseology  of 
which  every  word  is  a  theory  :   whereas  a  simple  and 
genuine  specification  of  the  phenomena  which  mark  a 
particular   disease;   a   specification   unsophisticated    by 
fancy,  or  by  preconceived  opinions,  may  be  regarded  as 
unequivocal  evidence  of  a  mind  trained  by  long  and 
successful  study  to  the  most  difficult  of  all  arts,  that  of 
the  faithful  interpretation  of  nature." ' 

No  better  instance  of  the  Fallacy  of  Mal-observation 
can  be  given  than  what  was  called  the  common-sense 
argument  against  the  truth  of  the  Copernican  System. 


TO  INDUCTION, 


'^75 


That  the  earth  should  move  round  the  sun,  men  said,  was 
impossible ;  for,  every  day,  they  saw  the  sun  rise  and  set 
and  perform  his  course  in  the  heavens.  They  felt  the 
earth  at  rest,  they  saw  the  sun  in  motion,  and  it  was 
absurd  to  call  upon  them  to  disbelieve  the  direct  evidence 
of  their  senses.  It  need  hardly  be  said  that  what  they 
mistook  for  the  direct  evidence  of  their  senses  was  really 
an  inference.  What  they  saw  was  consistent  with  one 
or  other  of  two  hypotheses,  that  the  sun  moved,  or  that 
the  earth  moved ;  and,  neglecting  to  take  any  account  of 
the  latter,  they  assumed  the  former.  If  it  were  not  for 
the  impressions  of  a  contrary  kind  derived  from  the 
actual  motion  of  the  carriage,  a  man,  whirled  along  in 
a  railway  train,  might  with  equal  justice  maintain,  by  an 
appeal  to  the  evidence  of  his  eyesight,  that  the  trees  and 
the  houses  were  running  past  him. 

Ventriloquism  supplies  another  familiar  instance  of  the 
same  error.  A  man  who  had  never  before  been  imposed 
upon  by  the  tricks  of  a  ventriloquist,  and  who  was  not 
aware  of  the  character  of  the  deception,  would  be  positive 
in  maintaining  that  he  had  the  direct  evidence  of  the 
sense  of  hearing  in  support  of  his  belief  that  the  sound 
he  heard  proceeded  from  a  particular  person  or  a  par- 
ticular part  of  the  building  other  than  that  from  which  it 
really  came.  The  fact,  of  course,  is  that  the  sound  itself  is 
all  that  is  directly  perceived  by  the  sense  of  hearing ;  the 
reference  of  it  to  a  particular  person  or  a  particular  place 
is  an  act  of  inference  grounded  upon  constant,  or  at 
least  frequent,  association.     What  is  done  by  the  ven- 

T  2 


2^6 


FALLACIES  INCIDENT 


triloquist  is  not  to  deceive  the  sense  of  hearing,  but  to 
mislead  the  faculty  of  judgment. 

What  are  called  '  delusions '  and  *  hallucinations '  fur- 
nish a  further  instance  of  Mal-observation.     It  seems  to 
be   now  pretty  generally  agreed  that  these  are  due  to 
morbid  affections  of  the  sensory  ganglia.     '  The  patient's 
senses,'  says  Dr.  Maudsley2^  speaking  of  what  he  calls 
sensorial  insanity,  '  are  possessed  with  hallucinations,  their 
ganglionic  central  cells  being  in  a  state  of  convulsive 
action;  before  the  eyes  are  blood-red  flames  of  fire,  amidst 
which  whosoever  happens  to  present  himself,  appears  as 
a  devil,  or  otherwise  horribly  transformed ;  the  ears  are 
filled  with  a  terrible  roaring  noise,  or  resound  with  a  voice 
imperatively  commanding  him  to  save  himself;  the  smell 
is  perhaps  one  of  sulphurous  stifling ;  and  the  desperate 
and  violent  actions  are,  like  the  furious  acts  of  the  ele- 
phant, the  convulsive  reactions  to  such  fearful  halluci- 
nations.    The  individual  in  such  a  state  is  a  machine  set 
in  destructive  motion,  and  he  perpetrates  the  extremest 
violence  or  the  most  desperate  murder  without  conscious- 
ness at  the  time,  and  without  memory  of  it  afterwards.' 
What  is  here  said  of  delusions  in  that  extreme  form  in 
which  they  assume  unmistakeably  the  character  of  mad- 
ness applies  equally,  as   an   explanation,  to  those  less 
obtrusive,  though  far  more  frequent,  forms  in  which  they 
produce  semi-insanity,  monomania,  melancholy,  or  par- 
tial and  temporary  deception.     In   all  these  cases,  the 
"^  Maudsley,   The  Physiology  and  Pathology  of  Mind,  ch.  iv.  p. 


lOI. 


TO  INDUCTION 


277 


sensations  are  really  experienced  ;  the  error  consists  in 
referring  the  cause  of  the  sensations  to  external  objects 
rather  than  to  the  morbid  condition  or  action  of  the 
brain  itself.  The  testimony  of  others,  or  the  inherent 
improbability  of  the  things  perceived,  ought  to  be  re- 
garded, though  they  seldom  are,  as  sufficient  proof  that 
the  evidence  of  the  senses  is  given  under  abnormal  and 
untrustworthy  conditions. 

To  the  head  of  Mal-observation,  or  the  substitution 
of  gratuitous  inference  for  accurate  observation,  may  be 
referred  the  fallacy  which  may,  perhaps,  best  be  designated 
as  Exaggerated  Comparison.  By  the  side  of  anything 
very  large,  we  are  apt,  being  prepossessed  by  the  idea  of 
largeness,  to  suppose  that  a  small  object  is  smaller  than 
it  really  is,  and,  on  the  other  hand,  by  the  side  of  any- 
thing very  small,  being  prepossessed  by  the  idea  of  small- 
ness,  that  a  large  object  is  larger  than  it  really  is. 
Similarly,  of  things  bright  or  dark,  of  periods  and 
distances  long  or  short,  of  actions  good  or  evil,  of 
evidence  probable  or  improbable,  and  the  like.  We 
are  all  familiar  with  the  '  only  half  a  mile  off,'  when  we 
are  approaching  a  town,  which  we  shall  probably  find  to 
be  at  least  double  or  treble  the  distance  named.  The 
countryman,  of  whom  we  enquire,  knows  that,  in  com- 
parison with  long  distances,  the  distance  is  short,  and 
then,  unconsciously  exaggerating  the  shortness  of  the 
distance,  proceeds  to  name  some  definite  distance  which, 
in  his  mind,  is  typical  of  shortness  or  which,  he  thinks, 
will  sufficiently  reassure  the  weary  traveller.     Instead  of 


278 


FALLACIES  INCIDENT 


recurring  to  his  own  actual  experience  of  the  time  he 
takes  to  walk  it,  he  draws  a  rapid  inference  from  the 
fact   that   the   distance   is   comparatively   short   to   the 
particular  distance  which  he  names.     In  the  same  way, 
men  are  apt  to  underrate  the  probability  of  an  argument 
as   compared  with   certainty  or  a  very  high  degree  of 
probability,  or,  on  the  other  hand,  to  overrate  its  proba- 
bility, as  compared  with  very  faint  indications  of  evidence. 
The  concentration  of  our  attention  on  one  term  of  the 
comparison  perverts  our  judgment  with  reference  to  the 
other  term. 

The  description  here  given  of  the  errors  originating 
in  Non-observation  or  Mal-observation  includes,  as  will 
already  have  been  perceived,  the  errors  incident  to  arti- 
ficial as  well  as  to  natural  observation,  that  is,  to  experi- 
ment as  well  as  to  observation  proper. 

III.    The  errors   incidental    to  the  other  operations 
preliminary  to  induction,  namely,  classification,  nomen- 
clature,  terminology,  and  hypothesis,  will  be  sufficiently 
apparent  on  a  perusal  of  the  sections  appropriated  to 
the  discussion  of  those  processes.     In  the  steps  inter- 
mediate between  the  observation  of  individual  facts  and 
the  inductive  inference   itself,  it  is  in  the  employment 
of  artificial   instead   of  natural   classifications,    and    in 
the  neglect  of  the  rules  designed  to  guard  against  the 
formation  of  illegitimate  hypotheses,  that  the  danger  of 
error  mainly  lies. 


TO  INDUCTION 


279 


B.  The  fallacies  incidental  to  the  performance  of  the 
inductive  process  itself  may  be  called  Fallacies  of  General- 
isation. An  error  of  this  class  is  committed  whenever, 
in  arguments  grounded  on  experience,  we  overrate  the 
value  of  the  evidence  before  us ;  that  is,  whenever  we 
accept  an  imperfect  induction  as  a  perfect  one,  or  when- 
ever, in  an  induction  confessedly  imperfect,  we  under- 
estimate the  amount  of  imperfection. 

Of  the  imperfect  inductions,  the  argument  from  analogy 
is  little  likely  to  be  mistaken  for  a  perfect  induction.  The 
strength  of  the  analogy  is  often  grossly  exaggerated,  and 
an  argument  which  possesses  little  or  no  probability  is 
often  adduced  as  affording  highly  probable  evidence  ;  but, 
as  this  kind  of  argument  is  very  seldom  -'  treated  as 
affording  absolute  certainty,  the  discussion  of  false  ana- 
logies may  be  reserved  till  I  have  completed  the  treat- 
ment of  the  other  errors  which  consist  in  regarding 
imperfect  as  perfect  inductions. 

Excluding  analogy,  there  are,  as  we  have  seen,  two 
forms  of  imperfect  induction,  that  which  employs  the 
incomplete  Inductio  per  Enumerationem  Simplicem  and 
that  which  consists  in  an  imperfect  fulfilment  of  the 
conditions  of  the  inductive  methods.  An  argument 
of  either  of  these  classes  may  be,  and  frequently 
is,    mistaken    for   a   perfect    induction.      I    shall    first 


21  The  geological  example  on  p.  236  may  perhaps  be  an  instance 
of  an  analogical  argument  thus  regarded.  Many  writers  have 
certainly  treated  the  inference  as  if  its  certainty  admitted  of  no 
doubt. 


28o  FALLACIES  INCIDENT 

notice  the  case  in  which  scientific  induction  is  simu- 
lated by  the  incomplete  Inductio  per  Enumerationem 
Simplicem  ^^ 

IV.  When  men  first  begin  to  argue  from  their  experi- 
ence of  the  past  to  their  expectation  of  the  future,  or  from 
the  observation  of  what  immediately  surrounds  them  to 
the  properties  of  distant  objects,  they  seem  naturally  to 
fall  into  this  unscientific  and  unreflective  mode  of  reason- 
ing.    They  have  constantly  seen  two  phenomena  in  con- 
junction, and,  consequently,  they  cannot  imagine  them  to 
be  dissevered,  or  they  have  never  seen  two  phenomena 
in  conjunction,  and,  consequently,  they  cannot  imagine 
them  to  be  associated.     The  difficulties  experienced  by 
children   in   accommodating   their   conceptions   to   the 
wider  experiences  of  men  ;  the  tendency  of  the  unin- 
structed,  and  frequently  even  of  the  instructed,  to  invest 
with  the  peculiar  circumstances  of  their  own  time  or 
country  the  men  of  a  former  generation  or  of  another 
land  ;  the  prejudices  entertained  against  those  of  another 
creed,  or  party,  or  nationality,  as  if  moral  excellence 
were    never    dissociated  from  particular  opinions  or  a 
particular   lineage,-are    all    evidences   of  the   limited 
character   of  our   first   efforts   at  generalisation.     It  is 
long   before   men   learn   to    discriminate    between   the 

«  The  student  who  has  read  the  first  and  fourth  Chapters  hardly 
needs  to  be  reminded  that  there  are  cases,  however,  in  which  the 
method  of  Inductio  per  Enumerationem  Simplicem  may,  or  even 
must,  be  employed,  'ilie  fallacies  here  treated  are  due  to  the  un- 
necessary or  injudicious  employment  of  the  method. 


TO  INDUCTION 


281 


material  and  immaterial  circumstances  attendant  on 
any  given  phenomenon,  to  perceive  the  irrelevancy  of 
the  immaterial  circumstances,  and  to  recognise  the 
necessity  of  insisting  on  a  repetition  of  all  the  material 
circumstances  before  they  anticipate  a  similar  effect. 
But  not  only  is.  the  Inductio  per  Enumerationem  Sim- 
plicem the  mode  of  generalisation  natural  to  immature 
and  uninstructed  minds ;  it  is  the  method  which,  till  the 
time  of  Bacon  '^  or  at  least  till  the  era  of  those  great 
discoveries  which  shortly  preceded  the  time  of  Bacon, 
was  almost  universal.     Aristotle,  it  is  true,  usually  ^^  (for 

«  Bacon  seems  to  be  never  weary  of  condemning  this  unscient  fie 
procedure.  Thus,  in  addition  to  the  aphorism  already  quoted  (p. 
125),  we  have,  amongst  others,  the  following  emphatic  passages: 
*  Axiomata  qua;  in  usu  sunt  ex  tenui  et  maiiipulari  experientia,  et 
paucis  particularibus,  quae  ut  plurimum  occurrunt,  fluxere ;  et  sunt 
fere  ad  mensuram  eorum  facta  et  extensa :  ut  nil  mirum  sit,  si  ad 
nova  particularia  non  ducant.  Quod  si  forte  instantia  aliqua,  non 
prius  animadversa  aut  cognita,  se  offerat,  axioma  distinclione  aliqua 
frivola  salvatur,  ubi  emendari  ipsum  verius  ioxtX-.'—Nov.  Org.  Lib.  I. 
Aph.  XXV.  '  At  philosophioe  genus  empincum  placita  magis  deformia 
et  monstrosa  educit,  quam  sophisticum  aut  rationale  genus  ;  quia  non 
in  luce  notionum  vulgarium  (quae  licet  tenuis  sit  et  superficialis, 
tamen  est  quodammodo  universalis,  et  ad  multa  pertinens)  sed  in 
paucorum  experimentorum  angustiis  et  obscurilate  fundatum  est. .  .  . 
Sed  tamen  circa  hujusmodi  philosophias  cautio  nuUo  modo  praeter- 
mittenda  erat ;  quia  mentejam  praevidemus  et  auguramur,  si  quando 
homines,  nostris  monitis  excitati,  ad  experientiam  se  serio  contulerint 
(valere  jussis  doctrinis  sophisticis\  tum  demum,  propter  praematuram 
et  prseproperam  intellectus  festinationem  et  saltum  sive  volatum  ad 
generalia  et  rerum  principia,  fore  ut  magnum  ab  hujusmodi  philo- 
sophiis  i^ericulum  immineat ;  cui  malo  etiam  nunc  obviam  ire 
debemus.'— Aph.  Ixiv. 

»'  For  exceptions,  see-4«.  Post.  I.  31,  p.  88,  a.  4-5  ;   Top.  VIII.  8, 


282 


FALLACIES  INCIDENT 


he  is  not  consistent  on  this  point)  requires  that  an  in- 
duction should  be  based  on  an  examination  of  all  the 
instances  ;  but  this  requirement  being  in  the  vast  majority 
of  cases  (even  if  we  suppose  Aristotle  to  be  speaking  of 
species  rather  than  individuals)  impossible  of  fulfilment, 
he  was  obliged,  whenever  he  had  recourse  to  experience, 
to   content  himself  with  an  inspection  of  those  cases 
which   were  nearest  at  hand.     Thus,  in  the  very  pas- 
sage ^•^'  in  which  he  emphatically  asserts  that  the  minor 
premiss   of  the  inductive  syllogism  (for   he  represents 
induction  under  the  syllogistic  form)  should  include  all 
the  instances,  he  argues  that  all  animals  which  are  de- 
ficient in  bile  are  long-lived,  because  he  finds  this  to  be 
the  case  with  the  man,  the  horse,  and  the  mule.     Aris- 
totle's works,  and  especially  those  on  Natural  History, 
abound  in  rash  generalisations  of  this  kind.     'It  is  a 
fact,'  says  Mr.  Lewes  ^   '  that  normally  in  turtles,  and 
exceptionally  in  elephants,  horses,  and  oxen,  there  is  an 
ossification  of  the  septum  of  the  heart.     Aristotle  saw  or 
heard  of  one  of  these  "  bones  "  in  the  hearts  of  a  horse 
and  an  ox,  and  forthwith  generalised  the   observation 
n   1 60,  b.  3.     For  further  information  on  Aristotle's  theory  of  Induc- 
tion  I  must  refer  the  student  to  the  be^nnning  of  §  13,  and,  for  a 
more  detailed  account  of  the  causes  of  his  failure  in  his  physical 
researches  than  can  well  be  given  here,  to  §  1 1  of  the  Introduction 
to  my  edition  of  Bacon's  Novum  Organum. 
«■•  Analytic  a  Prior  a,  ii.  25. 

■^  I^wes'  Aristotle,  ch.  xvi.  §  399-  ^n  the  other  hand,  the  student, 
who  is  interested  in  the  history  of  science,  will  do  well  to  read,  in 
arrest  of  judgment  on  Aristotle,  Dr.  William  Ogle's  Introduction  to 
his  translation  of  the  De  Partibus  Animalium, 


TO  INDUCTION, 


283 


thus  :  "The  heart  is  destitute  of  bones  except  in  horses 
and  in  a  species  of  ox ;  these,  however,  in  consequence 
of  their  size,  have  something  bony  as  a  support,  just  as 
we  find  throughout  the  whole  body'^'^."  His  Spanish 
follower  Funes  Y  Mendo9a  improves  on  this  statement 
by  saying  that  the  bone  acts  like  a  stick  to  support  the 
weight  of  the  heart,  which  is  very  great.' 

There  is  another  passage  in  which  Aristotle  tells  us 
that  the  cranium  of  a  dog  consists  of  a  single  bone  ^^ 
'  It  is  probable,'  says  the  author  of  the  review  previously 
quoted  ^',  *  that  Aristotle  had  got  hold  of  the  cranium 
of  an  old  individual  in  which  the  sutures  had  become 
obliterated.' 

The  employment  of  the  Inductio  per  Enumerationem 
Simplicem  prevailed  so  universally  from  the  time  of 
Aristotle  to  the  rise  of  modern  science  that  it  seems 
unnecessary  to  multiply  instances  of  it  during  that  period. 
But  it  may  be  instructive  to  illustrate  from  the  history 
of  more  recent  times  the  peculiar  facility  with  which 
some  even  of  the  greatest  discoverers  have  lapsed  into 
this  erroneous  form  of  reasoning. 

*Bichat,'  says  Mr.  Lewes'^  *  tried  to  establish  a  gene- 
ralisation which  has  been  much  admired,  namely,  that  all  the 

■■'^  De  Partibus  Animalium,  Bk.  III.  ch.  iv. 

'*  ra  u(v  yap  ex**  fiovvarfov  to  Kpaviov,  wanfp  6  kvcvv,  to.  5^  crvy- 
Keifjifvov,  uffiTfp  dvOpojiros. — Historia  A7iimaliu7n,  Bk.  III.  ch.  vii. 

*>  Quarterly  Review,  No.  233,  Art.  ii.  The  mention  of  the  human 
skull,  which  had  no  sutures,  is  evidently  borrowed  from  Herodotus, 
IX.  83. 

"^  Lewes'  Aristotle^  ch.  xvi.  §  399  d. 


284 


FALLACIES  INCIDENT 


organs  of  Animal  life  are  double  and  symmetrical,  while  all 
the  organs  of  Vegetal  life  are  single  and  asymmetrical. 
Unhappily  the  facts  do  not  fit.  In  the  commencement 
almost  n^ery  organ  is  double  and  symmetrical ;  and  only  in 
the  later  stages  of  development  do  the  differences  appear. 
Even  in  the  matured  organism  we  find  many  striking  ex- 
ceptions to  Bichat's  generalisation.  Thus  the  parotid, 
sublingual,  and  mammary  glands,  the  lungs,  the  kidneys, 
ovaries,  and  testes,  are  all  vegetal  organs,  and  all  generally 
double.  And  if  the  heart  and  uterus  are  classed  as  smgle 
organs,  then  must  the  brain  and  spinal  cord  be  classed  thus. 
While  in  birds  the  liver  is  double  and  symmetrical.' 

Mt   is   in  a  great  degree  true,'  we  are  informed  by  Dr. 
Parish's  *that  the  sensible  qualities  of  plants,  such  as  colour, 
taste,  and  svull,  have  an  intimate  relation  to  their  properties, 
and  may  often  lead  by  analogy  to  an  indication  of  their 
powers  ;  we  have  an  example  of  this  in  the  dark  and  gloomy 
aspect  of  the  Luridce,  which  is  indicative  of  their  narcotic 
and    very    dangerous    qualities,    as    Datura,    Hyoscyamus, 
Alropa,  and  Nicotiana.     Colour  is  certainly  in  many  cases  a 
test  of  activity  ;  the  deepest  of  coloured  flowers,  the  Digitalis, 
for  example,  are  the  most  active,  and  when  the  leaves  of 
powerful  plants  lose  their  green  hue,  we  may  conclude  that  a 
corresponding  deterioration  has  taken  place  with  respect  to 
their  virtues  :  but  Linnaeus  ascribes  too  much  importance  to 
such  an  indication,  and  his  aphorisms  are  unsupported  by 
facts;    for   instance,   he   says,   "Color    pallidus   insipidum, 
viridi's  crudum,  luteus  amarum,  ruber  acidum,  albus  duke, 
niger  ingratum,  indicat." ' 

The  early  history  of  Geology  presents,   in  the  con- 
troversy which  was  long  carried  on  between  the  Nep- 
tunians  and   Vulcanians,  a  remarkable  instance  of  the 
3»  Pharmacologia^  ninth  ed.  pp.  iio,  iii. 


TO  INDUCTION, 


285 


errors  arising  from  a  partial  induction,  as  well  as  of  the 
tenacity  with  which  men  will  cling  to  views  to  which  they 
have  once  committed  themselves.  The  Neptunians,  the 
student  need  hardly  be  told,  referred  all  geological  phe- 
nomena to  the  influence  of  water,  while  the  Vulcanians 
greatly  exaggerated  the  action  of  heat  in  the  past  his- 
tory of  the  globe,  and  multiplied  to  an  excess  the  number 
of  formations  to  be  ascribed  to  an  igneous  origin.  Of 
the  Neptunians,  the  great  Saxon  geologist  Werner  was 
the  chief. 

*  Werner,'  says  Sir  Charles  Lyell '-, '  had  not  travelled  to 
distant  countries  ;  he  had  merely  explored  a  small  portion  of 
Germany,  and  conceived,  and  persuaded  others  to  believe, 
that  the  whole  surface  of  our  planet,  and  all  the  mountain 
chains  in  the  world,  were  made  after  the  model  of  his  own 
province.  It  became  a  ruling  object  of  ambition  in  the  minds 
of  his  pupils  to  confirm  the  generalisations  of  their  great 
master,  and  to  discover  in  the  most  distant  parts  of  the 
globe  his  "universal  formations,"  which  he  supposed  had 
been  each  in  succession  simultaneously  precipitated  over  the 
whole  earth  from  a  common  menstruum  or  "  chaotic  fluid." 
It  now  appears  that  the  Saxon  professor  had  misinterpreted 
many  of  the  most  important  appearances  even  in  the  im- 
mediate neighbourhood  of  Freyberg.  Thus,  for  example, 
within  a  day's  journey  of  his  school,  the  porphyry,  called  by 
him  primitive,  has  been  found  not  only  to  send  forth  veins  or 
dikes  through  strata  of  the  coal  formation,  but  to  overlie  them 


m  mass. 


*  In  regard  to  basalt  and  other  igneous  rocks,  Werner's 
theory  was  original,  but  it  was  also  extremely  erroneous. 

w  Lyell's  Principles  of  Geolog)'^  ninth  ed.  Bk.  I.  ch.  iv. 


286 


FALLACIES  INCIDENT 


The  basalts  of  Saxony  and  Hesse,  to  which  his  observations 
were  chiefly  confined,  consisted  of  tabular  masses  capping  the 
h^lls,  and  not  connected  with  the  levels  of  existing  valleys 
like  many  in  Auvergne  and  the  Vivarais.  These  basalts,  and 
all  other  rocks  of  the  same  family  in  other  countries,  were, 
according  to  him,  chemical  precipitates  from  water.  He 
denied  that  they  were  the  products  of  submarine  volcanoes ; 
and  even  taught  that,  in  the  primeval  ages  of  the  world,  there 
were  no  volcanoes.' 

After  describing  the  complete  demolition  of  this  theory 
by  some  of  Werner's  contemporaries.  Sir  Charles  Lyell 
adds : — 

*  Notwithstanding  this  mass  of  evidence,  the  scholars  of 
Werner  were   prepared  to   support   his  opinions    to  their 
utmost  extent ;  maintaining,  in  the  fulness  of  their  faith,  that 
even  obsidian  was  an  aqueous   precipitate.     As  they  were 
blinded  by  their  veneration  for  the  great  teacher,  they  were 
impatient  of  opposition,  and  soon  imbibed  the  spirit  of  a 
faction  ;  and  their  opponents,  the  Vulcanists,  were  not  long 
in  becoming  contaminated  with  the  same  intemperate  zeal. 
Ridicule  and  irony  were  weapons  more  frequently  employed 
than  argument  by  the  rival  sects,  till  at  last  the  controversy 
was  carried  on  with  a  degree  of  bitterness  almost  unprece- 
dented in  questions  of  physical  science.     Desmarest  alone, 
who  had  long  before  provided  ample  materials  for  refuting 
such  a  theory,  kept  aloof  from  the  strife  ;   and,  whenever 
a  zealous  Neptunist  wished  to  draw  the  old  man  into  an 
argument,  he  was  satisfied  with  replying  "  Go  and  see."  ' 

In  the  Science  of  Probability,  there  is  an  interesting 
example  of  the  unreflecting  application  of  the  Inductio 
per   Enumerationem   Simplicem.      Averages  of  a  suffi- 


TO  INDUCTION. 


287 


ciently  trustworthy  character  can  often  be  struck  as  to 
the  frequency  of  such  events  as  the  number  of  deaths, 
the  number  of  suicides,  the  number  of  lost  letters  which 
occur  in  a  year.  But  the  least  reflexion  ought  to  show 
that  the  accuracy  of  these  calculations  depends  on  the 
assumption  that  the  causes  in  operation,  so  far  as  they 
aff*ect  these  events,  will  continue  to  be  much  the  same 
as  at  present.  This,  however,  is  a  consideration  which 
is  frequently  lost  sight  of,  and  thus  averages,  which  may 
be  perfectly  true  within  certain  limits  and  on  certain 
hypotheses,  are  extended,  as  if  they  were  true  univer- 
sally and  unconditionally.  Mr.  Venn,  in  his  w^ork  on 
the  Logic  of  Chance^\  has  drawn  especial  attention  to 
this  source  of  error.  The  following  passage  selected 
from  that  work  will,  perhaps,  aff'ord  a  sufificient  illus- 
tration of  the  point  in  question  : — 

*  Let  us  take,  for  example,  the  average  duration  of  life. 
This,  provided  our  data  are  sufficiently  extensive,  is  known 
to  be  tolerably  regular  and  uniform.  But  a  very  little  con- 
sideration will  show  that  there  may  be  a  superior  as  well  as 
an  inferior  limit  to  the  extent  within  which  this  uniformity 
can  be  observed.  At  the  present  time  the  average  duration 
of  life  in  England  may  be,  say  thirty ;  but  a  century  ago  it 
was  decidedly  less  ;  several  centuries  ago  it  was  very  much 
less  ;  whilst,  if  we  possessed  statistics  referring  to  our  early 
British  ancestors,  we  should  probably  find  that  there  has  been 
since  that  time  a  still  more  marked  improvement.  What 
may  be  the  future  tendency  no  man  can  say  for  certain.  It 
may  be,  and  we  hope  will  be  the  case,  that,  owing  to  sanitary 

^  Venn's  Logic  of  Chance^  chap.  i. 


288 


FALLACIES  INCIDENT 


and  other  improvements,  the  duration  of  l.fe  w.ll  go  on 
increasing  steadily;  it  is  quite  conceivable  that  U  shouW  do 
so  without  limit.     On  the  other  hand,  th.s  duration  mgl 
gradually  tend  towards  some  fixed  length.     Or,  agam   >    .s 
perfectly  possible  that  future  generations  might  prefer  a 
short  and  a  merr>-  life,  and  therefore  reduce  the.r  average. 
All  Ihat  I  am  concerned  to  indicate  is,  that  th.s  uniformity 
(as  we  have  hitherto  called  it)  has  varied,  and,  under  the  m- 
fluence  of  future  eddies  in  opinion  and  practice,  may  vary 
still  ;    and  this   to   any  extent,  and  with   any  degree   of 
irregularity.    To  borrow  a  term  from  Astronomy,  we  find 
Ir  uniformity  subject  to  what  might  be  called  an  irregular 

j^^///ar  variation.  *o^*.n 

'  The  above  is  a  fair  typical  instance.     If  we  had  taken 
a  less  simple  feature  than  the  length  of  life,   or  one  less 
closely  connected  with  what  may  be  called  the  great  per- 
n.anent   uniformities  of  nature,  we  should  have  found    he 
peculiarity  under  notice  exhibited   m  a  far   more  str  k  ng 
degree.     The  deaths  from  small-pox,  for  example    o     the 
instances   of  duelling   or   accusations    of  witchcraft,    f  ex- 
amined during  a  few  successive  years,  would  have  shown 
:  vLy  toleraMe  degree  of  uniformity.     But  th,s  umforrn.y 
has  risen  probably  from  zero  ;  after  various  and  very  great 
fluctuations  seems   tending  towards  zero  agam  ;  and  may 
or  anything  we  know,  undergo  still  greater  fluctuations  m 
Ire.'  Now  these  examples  I  consider  to  be  only  extreme 
ones,  and  not  such  very  extreme  ones,  of  what  ,s  the  almos 
univ;rsal  rule  in  nature.      I  shall  endeavour  to  shew    ha 
even  the  few  apparent  exceptions,  such  as  the  P-portions 
between   male   and   female   births,  &c.,   may   not   be,   and 
probably  in  reality  are  not,  exceptions.    A  type  that  isjer- 
sistent  and  invariable  is  scarcely  to  be  found  m  nature  . 
In   these  and  similar  cases,  the  fallacy  arises   from 
3«  Venn's  Logic  of  Chance,  ch.  i.  sect.  lo,  ii. 


TO  INDUCTION, 


289 


supposing  that  mere  frequency  of  occurrence  affords  a 
sufficient  guide  to  inference,  without  reflecting  that  the 
events  depend  on  causes,  and  that,  if  the  causes  vary, 
the  character  of  the  events  must  vary  with  them. 

Sometimes,  frequency  of  occurrence,  instead  of  furnish- 
ing an  argument  for  the  recurrence  of  an  event,  ought, 
if  we  duly  reflect  on  the  natural  action  of  causes,  actually 
to  furnish  an  argument  against  it.  Thus,  a  miner,  in- 
stead of  trusting  to  his  rope,  because  it  has  served  him 
so  often,  ought  actually  to  distrust  it,  because  it  has 
been  strained  so  much ;  a  prodigal,  who  has  frequently 
succeeded  in  borrowing  from  his  friends,  ought  to  begin 
to  suspect  that  their  patience  may  be  exhausted  ;  a  timid 
man,  who  has  on  one  or  two  occasions  aroused  his 
neighbours  by  a  false  alarm,  instead  of  arguing  from 
experience  that  they  will  come  to  his  rescue  again,  ought 
rather  to  expect  that,  warned  by  the  past,  they  will 
remain  comfortably  in  their  beds.  It  cannot  be  too 
often  repeated,  that  we  ought  never  to  depend  on  fre- 
quency of  occurrence,  wherever  it  is  possible  to  have 
recourse  to  facts  of  causation. 

It  is  remarked  by  Mr.  Mill  that  the  Method  of  Simple 
Enumeration,  though  almost  banished  from  the  physical 
sciences,  is  still  the  common  and  received  method  of 
induction  in  whatever  relates  to  man  and  society.  The 
reason  of  this  remark  is  to  be  sought  in  the  extraordinary 
difficulty  of  subjecting  this  class  of  speculations  to  the 
more  scientific  methods.  Moral  and  social  phenomena 
are   so   complex  that  it  is  often  next  to  impossible   to 

u 


290 


FALLACIES  INCIDENT 


discover  by  elimination  the  true  connexion  between  any 
two  events  or  sets  of  facts.     Take,  for  instance,  such 
questions   as   the   influence  of  any   particular   form   of 
government   upon   the  welfare   of   the    people   among 
whom  it  is  established,  the  effects  of  religion,  or  of  any 
particular  form  of  religion,  upon  morals,  the  social  and 
political  conditions  most  favourable  to  the  developmen 
of  art  or  literature  or  science  or  commerce.     Here,  it  it 
be  required  to  discover  the  cause  of  a  given  effect,  our 
materials  are  a  set  of  consequents  constantly  varying  in 
their  character  and  intensity,  and  a  set  of  antecedents, 
often  verv  numerous,  any  one  of  which  may   have   an 
appreciable  influence  in  the  production  of  the  effect  in 
qviLstion ;  and  it  is  obvious  that  to  detect  the   precise 
decree  in  which  the  effect  is  due  to  any  one  of  these 
antecedents,  even  supposing  the  task  to  be  possible,  will 
require  the  utmost  skill,  patience,  and  dispassionateness 
in  the  selection  and  comparison  of  instances.     Nor,  if 
it  be  required  to  discover  the  effect  of  a  given  cause, 
will  the  task  be  much  simplified  ;  for,  though  it  may  be 
possible  to  fix  the  precise  time  at  which  a  new  cause-- 
say  a  new  form  of  religion,  a  new  form  of  government, 
or  a  new  commercial  tariff-was  introduced,  yet,  before 
it  can  be  argued  that  any  novel  event  which  may  appear 
to  have  resulted  from  it,  is  really  due  to  it,  as  an  effect 
to   a   cause,  the   enquirer   is   bound   to  satisfy  himself 
(,)  that  the  introduction  of  the  new  cause  was  not  ac- 
companied by  other  causes  which  may  have  wholly  or 
.partially  produced  the  supposed  effect,  (2)  that  the  new 


TO  INDUCTION. 


291 


cause  and  the  supposed  effect  are  not  joint  effects  of 
some  common  cause  which   he  may  have   overlooked. 
It  is   the   extreme   difficulty  of  bringing  this  class  of 
questions  within  the  requirements  of  scientific  induction, 
that  has  led,  on  the  one  hand,  to  the  employment  of  the 
loose  Method  of  Inductio  per  Enumerationem  Simplicem, 
or  of  a  mere  appeal  to  unsifted  experience,  and  on  the 
other  to  the  disbelief  in  the  possibility  of  arriving  at  any 
satisfactory  conclusions  upon  them.     At  the  same  time, 
there  can  be  little  doubt  that  moral  and  social  enquiries 
are  beginning  to  emerge  from  the  chaotic  state  of  con- 
fusion in  which  they  have  hitherto  been  sunk,  and  that 
what  are  now  dignified  with  the  titles  of  the  moral  and 
political  sciences,  however  imperfect  they  may  be,  are 
beginning  to  be  something  more  than  mere  collections 
of  random  guesses,  or  conclusions  drawn  from  the  first 
undisciplined  impressions  of  the  teaching  of  experience. 

To  the  class  of  fallacies  originating  in  the  employment 
of  the  incomplete  Inductio  per  Enumerationem  Sim- 
plicem may  perhaps  be  referred  the  illegitimate  use  of 
the  Argument  from  Authority.  The  opinions  or  pre- 
dictions of  a  certain  man  or  of  a  certain  class  of  men 
upon  some  particular  question  or  questions  have  been 
subsequently  found  to  be  verified  by  the  issue  of  events 
or  an  examination  of  the  facts.  From  this  circumstance 
it  is  sufficiently  rash  to  infer,  without  further  warrant, 
that  the  correspondence  between  these  predictions  or 
opinions  and  the  subsequent  events  or  ascertained  facts 
is   the   result   of  knowledge,  and   not  of  what  we  call 

u  2 


292 


FALLACIES  INCIDENT 


accident ;  but,   not  content  even  with  this  inference, 
men  are  apt  to  draw  the  far  more   unwarrantable  one 
that  this  person  or  class  of  persons  is  to  be  accepted 
a    an  authority  on  all  matters,  or  at  least  on  all  matters 
of  the  same  or  of  an  analogous  kind.     It  is  on  th>s 
principle  that  a  savage,  or  even  an  uneducated  man  m 
a  civilised  community,  will  trust  implicitly  any  person 
for  whom  he  has  conceived  a  general  respect.     In  nine 
cases  out  of  ten  he  probably  acts  more  wisely  m  trusting 
to  such  a  person  than  in  trusting  to  himself.     But  the 
same  habit  of  mind,  which  is  a  virtue  among  uneducated 
men  and  in  primitive  states  of  society,  becomes  one  of 
the  most  serious  obstacles  to  progress  and  knowledge 
when  men,  either  individually  or  collectively,  have   at- 
tained that  stage  at  which  they  are  able  to  enquire  for 
themselves.     We  have  to  learn  not  only  that  men  are 
to  be  trusted  exclusively  within  the  limits  of  their  own 
experience,  in  their  own  profession  or  pursuit,  but  that 
even  within  those  limits  their  authority  is  apt  to  become 
tyrannical  and  irrational    unless   it   is   constantly    con^ 
fronted   with   facts   and   subjected   to   the  criticism  of 

Others.  ,  .     .^ 

But  an  undiscriminating  submission  to  the  authority 

of  contemporaries,  of  which  I  have  hitherto  exclusively 
spoken,  has  been  but  a  shght  source  of  error  when  com- 
pared with  undiscriminating  submission  to  the  authority 
of  past  generations  -.  The  latter  involves  a  kmd  of  corn- 
s' Of  this  tendency  we  have  many  '  glaring  instances/  as  Bacon 
.ould  call  them.     The  error  has  been,  so  to  say,  canomsed  m  the 


TO  INDUCTION', 


293 


pound  fallacy.     The  authority  of  an  Aristotle  or  a  Galen 
has  come,  by  the  process  already  described,  to  be  re- 
ceived without  question  and  without  limit  by  his  own  or 
by  the  succeeding  generation ;   and  then,  by   the  con- 
stant repetition  of  a  similar  process,  it  is  received  from 
that  generation  by  the  leading  minds  of  the  next,  from 
them   by  their   contemporaries,  and  so  on,  respect  for 
tradition  being  blended  with  respect  for  a  great  name, 
and   both    these   resting   for   their   support  on  the  de- 
ference  paid   to   established   authority.     Many   of    the 
propositions   accepted   without   the   slightest   hesitation 
by  previous  generations  on  this  kind  of  authority  now 
appear    to   us  patently  absurd,  nor  is  it  without   effort 
that  we  can  realise  the  universality  of  their  former  re- 
ception ^\     Instances  of  such  propositions  have  already 

proverb  '  Mallem  cum  Platone  errare.'  There  is  a  characteristic 
aiecdote  of  Scheiner,  who  contests  with  Galileo  the  honour  of 
having  been  the  first  to  observe  the  spots  in  the  sun.  '  Schemer  was 
a  monk  ;  and,  on  communicating  to  the  superior  of  his  order  the 
account  of  the  spots,  he  received  in  reply  from  that  learned  father  a 
solemn  admonition  against  such  heretical  notions  :-- 1  have  searched 
through  Aristotle,"  he  said,  ''  and  can  find  nothing  of  the  kmd  men- 
tioned :  be  assured,  therefore,  that  it  is  a  deception  of  your  senses,  or 
of  your  glasses.'"- Baden  Powell's  History  of  Natural  Philosophy, 

^  36  xhe  increasing  unwillingness  of  men  to  accept  a  proposition  on 
mere  authority  is  thus  forcibly  put  by  Bentham,  Book  of  Fallacies 
Part  I.  ch.  i.,  first  published  in  French  by  M.  Dumont,  m  1815,  and 
in  English  by  '  A  Friend,'  in  1824. 

'  As  the  world  grows  older,  if  at  the  same  time  it  grows  wiser 
(which  it  will  do,  unless  the  period  shall  have  arrived  at  which  ex- 
perience, the  mother   of  wisdom,  shall   have  become  barren),  the 


294 


FALLACIES  INCIDENT 


been  given  under  the  head  of  the  Fallacies  of  Non- 
Observation,  to  the  production  of  which  class  of  fallacies 
the  undue  devotion  to  authority  has,  perhaps,  contributed 
more  than  any  other  cause ".  But,  in  subjects  lying 
remote  from  ordinary  observation,  propositions  almost 
equally  absurd  have  held  their  ground  till  quite  recently  ; 
some  continue  slill  to  maintain  themselves,  and  others  no 
doubt  will  be  propounded,  from  time  to  time,  to  take  ad- 
vantage of  the  credulity  of  mankind. 

*  To  give  a  general  currency,'  says  Dr.  Paris  '^  'to  a  hypo- 
influence  of  authority  will  in  each  situation,  and  particularly  in 
parliament,  become  less  and  less.' 

•  Take  any  part  of  the  field  of  moral  science,  private  morality, 
constitutional  law,  private  law  ;  go  back  a  few  centuries,  and  you 
will  find  argument  consisting  of  reference  to  authority,  not  exclu- 
sively, but  in  as  large  a  proportion  as  possible.  As  experience  has 
increased,  authority  has  been  gradually  set  aside,  and  reasoning, 
drawn  from  facts,  and  guided  by  reference  to  the  end  in  view,  true 
or  false,  has  taken  its  place. 

♦  *  ♦  *  * 

<  In  mechanics,  in  astronomy,  in  mathematics,  in  the  new-bom 
science  of  chemistry-no  one  has  at  this  time  of  day  either  effrontery 
or  folly  enough  to  avow,  or  so  much  as  to  insinuate,  that  the  most 
desirable  state  of  these  branches  of  useful  knowledge,  the  most 
rational  and  eligible  course,  is  to  substitute  decision  on  the  ground  of 
authority  to  decision  on  the  ground  of  direct  and  specific  evidence.' 

^7  It  might  appear  that  the  illegitimate  use  of  the  Argument  from 
Authoritv  should  be  classed  amongst  the  Fallacies  of  Non-Observa- 
tion ;  but,  though  a  blind  devotion  to  authority  is  one  of  the  most 
powerful  'influences  in  leading  men  to  neglect  observation  and  ex- 
periment,  the  disposition  to  bow  thus  unduly  to  it  is  itself  a  fact  which 
requires  explanation,  and  one  which  it  is  here  attempted  to  explain. 
^  Dr.  Paris'  Pharmacolosici,  Introduction,  p.  76,  &c. 


TO  INDUCTION, 


295 


thetical  opinion,  or  medicinal  reputation  to  an  inert  sub- 
stance, nothing  more  is  required  than  the  talismamc  aid  of  a 
few  great  names  ;  when  once  established  upon  such  a  basis, 
ingenuity,  argument,  and  even  experiment,  may  open  their 
ineffectual  batteries  ;  the  laconic  sentiment  of  the  Romai 
satirist  is  ever  opposed  to  remonstrance  :-^^  Marcus  dtx.f 
it  a  cstr     A   physician   cannot  err  in  the  opinion  of  the 
public,  if  he  implicitly  obeys  the  dogmas  of  authority.     In 
the  most  barbarous   ages   of  ancient  Egypt,  he  was  pun- 
ished  or  rewarded  according  to  the  extent  of  his  success ; 
but  to  escape  the  former  it  was  only  necessary  to  show  that 
an  orthodox  plan  of  cure  had  been  followed,  such  as  was 
prescribed  in  the  acknowledged  writings  of  Hermes.     It  is 
an  instinct  in  our  nature  to  follow  the  track  pointed  out  by 
a  few  leaders ;  we  are  gregarious  animals,  in  a  moral  as  wed 
as  a  physical  sense,  and  we  are  addicted  to  routine  because 
it  is  always  easier  to  follow  the  opinions  of  others  than  to 
reason  and  judge  for  ourselves ;  and  thus  do  one  half  of  the 
world  live  as  alms-folk  on  the  opinions  of  the  other  half. 
What  but  such  a  temper  could  have  upheld  the  preposterous 
system  of  Galen  for  more  than  thirteen  centuries,  and  have 
enabled  it  to  give  universal  laws  in  medicine  to  Europe, 
Africa,  and  part  of  Asia?    What  but  the  spell  of  authority 
could  have  inspired  a  general  belief  that  the  sooty  washings 
of  resin  could  act  as  a  universal  remedy  ?     What  but  a  blind 
devotion  to  authority,  or  an  insuperable  attachment  to  estab- 
lished custom  and  routine,  could  have  so  long  preserved  from 
oblivion  the  absurd  medicines  which  abound  in  our  earlier 
dispensatories?  for  example,  the  ^^ Decoctum  ad Iciertcos     of 
the  Edinburgh  College,  which  never  had  any  foundation  but 
that  of  the  doctrine  of  signatures  in  favour  of  the  Curcuma 
and  C/icIidonium  majusj  and  it  is  only  within  a  few  years 
that  the  T/iertaca  Andromachi,  in  its  ancient  form,  has  been 
dismissed  from  our  Pharmacopoeia.     The  CODEX  Medica- 
MENTARIUS  of  Paris  still  cherishes  the  many-headed  monster 


296 


FALLACIES  INCIDENT 


of  pharmacy,  under  the  appropriate  title  of  '' Electuarium 
Opiatum  Polypharmacwn^^  * 

*  The  same  devotion  to  authority  which  induces  us  to  re- 
tain an  accustomed  remedy  with  pertinacity,  will  frequently 
oppose  the  introduction  of  a  novel  practice  with  asperity, 
unless  indeed  it  be  supported  by  authority  of  still  greater 
weight  and  consideration.  The  history  of  various  articles 
of  diet  and  medicine  will  prove  in  a  striking  manner  how 
greatly  their  reputation  and  fate  have  depended  upon 
authority.  It  was  not  until  many  years  after  Ipecaciian 
had  been  imported  into  Europe,  that  Helvetius,  under  the 
patronage  of  Louis  XIV,  succeeded  in  introducing  it  into 
practice  :  and  to  the  eulogy  of  Katharine,  queen  of  Charles 
II,  we  are  indebted  for  the  general  introduction  of  tea  into 
England.' 

*  The  history  of  the  warm  bath  presents  us  with  another 
curious  instance  of  the  vicissitudes  to  which  the  reputation  of 
our  valuable  resources  is  so  universally  exposed  ;  that  which 
for  so  many  ages  was  esteemed  the  greatest  luxury  in  health, 
and  the  most  efficacious  remedy  in  disease,  fell  into  total 
disrepute  in  the  reign  of  Augustus,  for  no  other  reason  than 
because  Antonius  Musa  had  cured  the  emperor  of  a  dan- 
gerous malady  by  the  use  of  the  cold  bath.  The  most  frigid 
water  that  could  be  procured  was,  in  consequence,  recom- 
mended on  every  occasion :  thus  Horace,  in  his  epistle  to 
Vala,  exclaims — 

"  Caput  ac  stom.ichum  supponere  fontibus  audcnt 
Clusinis,  Gabiosque  petunt,  et  frigida  rura."— ^//V/.  xv.  lib.  i. 

*  This  practice,  however,  was  doomed  but  to  an  ephemeral 
popularity,  for,  although  it  had  restored  the  emperor  to 
health,  it  shortly  afterwards  killed  his  nephew  and  son-in- 
law,  Marcellus  ;  an  event  which  at  once  deprived  the  remedy 
of  its  credit  and  the  physician  of  his  popularity. 


TO  INDUCTION. 


297 


*  The  history  of  the  Peruvian  bark  would  furnish  a  very 
curious  illustration  of  the  overbearing  influence  of  authority 
in  giving  celebrity  to  a  medicine,  or  in  depriving  it  of  that 
reputation  to  which  its  virtues  entitle  it.   This  heroic  remedy 
was  first  brought  to  Spain  in  the  year  1632,  and  we  learn 
from  Villerobel   that  it  remained  for  seven  years   in   that 
country  before  any  trial  was  made  of  its  powers,  a  certain 
ecclesiastic  of  Alcala  being  the  first  person  in  Spain  to  whom 
it  was  administered  in  the  year  1639  ;  but  even  at  this  period 
its  use  was  limited,  and  it  would  have  sunk  into  oblivion  but 
for  the   supreme   power   of  the   Roman   church,  by  whose 
auspices  it  was  enabled  to  gain  a  temporary  triumph  over 
the  passions  and  prejudices  which  opposed  its  introduction. 
Innocent  the  Tenth,  at  the  intercession  of  Cardinal  de  Lugo, 
who  was  formeriy  a  Spanish  Jesuit,  ordered  that  the  nature 
and  eflfects  of  it  should  be  duly  examined,  and,  upon  being 
reported  as  both  innocent  and  salutary,  it  immediately  rose 
into  public  notice  ;  its  career,  however,  was  suddenly  stopped 
by  its  having  unfortunately  failed,  in  the  autumn  of  1652,  to 
cure  Leopold,  Archduke  of  Austria,  of  a  quartan  intermittent ; 
this  disappointment  kindled  the  resentment  of  the  prince's 
principal    physician,   Chifletius,   who    published    a    violent 
philippic   against   the  virtues  of  Peruvian   bark,  which   so 
fomented  the  prejudices  against  its  use,  that  it  had  neariy 
fallen  into  total  neglect  and  disrepute.' 

In  discussing  the  Argiunent  from  Authority,  I  have 
already  touched  on  i\\Q  Argument /ro?n  Universal  Consent. 
'This  is  a  proposition  to  which  we  cannot  refuse  our 
assent,  for  it  is  accepted  by  all  mankind.'  In  dealing 
with  this  argument,  w^e  must  always  ask,  first  of  all, 
whether  the  proposition  assented  to  expresses  an  im- 
mediate perception  or  an  inference.  If  it  expresses  the 
former,  we  cannot  call  it  in  question,  for  the  immediate 


298 


FALLACIES  INCIDENT 


perceptions  of  men  are  ultimate  facts,  true,  at  all  events, 
to  us,  and  admitting  of  no  further  test.  But  if  the  pro- 
position expresses  an  inference,  as,  for  instance,  in  the 
case  of  the  belief  in  the  motion  of  the  sun  round  the 
earth,  or  the  non-existence  of  antipodes,  we  must  pro- 
ceed to  ask  further  what  are  the  grounds  of  the  inference, 
and,  unless  the  grounds  of  the  inference  approve  them- 
selves to  us,  we  are  at  liberty  to  doubt  or  reject  it.  At 
the  same  time,  this  argument,  even  though  the  proposi- 
tion only  express  an  inference,  may  possess  considerable, 
if  not  overwhelming,  force,  provided  that  the  conclusion 
has  been  arrived  at  by  a  number  of  competent  persons 
after  due  examination,  and  as  a  result  of  independent 
investigation.  Even  here,  however,  the  true  authority  is 
that  of  the  competent  investigators,  not  that  of  their 
credulous  or  incompetent  followers  ^^  The  latter,  as  was 
once  said  by  the  late  Bishop  Thirlwall,  may  be  regarded 
as  the  ciphers  after  a  decimal  point  *^ 

V.  The  errors  incident  to  the  employment  of  the 
various  Inductive  Methods  have  already  been  pointed  out 

S'j  •  Verus  cnim  consensus  is  est,  qui  ex  libertate  judicii  (re  prius 
explorata)  in  idem  conveniente  consistit.  At  Humerus  lon<^c  maximus 
eorum,  qui  in  Aristotelis  philosophiam  consenseriint,  ex  pra?judicio 
et  auctoritatc  aliorum  se  illi  mancipavit ;  ut  sequacitas  sit  potius 
et  coilio,  quam  consensus.' — Bacon,  y\'<w.  Org.^Wh.  I.  Aph.  Ixxvii. 

***  Cp.  Glanvill's  Scepsis  Scicntifica,  ch.  xvii.  :  *  Authorities  alone 
with  me  make  no  number,  unless  Evidence  of  Reason  stand  before 
them  :  for  all  the  Cyphers  of  Arithmetic  are  no  better  than  a  single 
nothing.' 


TO  INDUCTION 


299 


in  my  detailed  description  of  each  of  these  Methods,  but 
it  may  be  useful  in  this  place  to  take  note  of  certain  forms 
of  fallacy  which  appear  to  be  common  to  them  all. 

The  Inductive  Methods  may  all  be  regarded  as  de- 
vices for  the  elimination  of  extraneous  circumstances  and 
for  the  establishment  of  a  causal  connexion  between  some 
two  phenomena,  a  and  b,  the  connexion  which  it  is  sought 
to  establish  being  generally  that  of  cause  and  effect. 
Now,  in  our  investigation,  we  may  either  have  mistaken 
the  precise  relation  between  a  and  ^,  or  we  may  have 
overlooked  some  other  material  circumstance  or  group 
of  circumstances,  c.  In  the  former  case,  the  most 
common  sources  of  error  are  either  the  inversion  of 
cause  and  effect  or  the  neglect  of  their  reciprocal  action, 
the  'mutuality  of  cause  and  effect,'  as  it  is  called  by 
Sir  G.  C.  Lewis.  In  the  latter  case  (supposing  a  to 
be  the  presumed  cause,  and  b  the  presumed  effect),  it 
seems  open  to  us  to  have  committed  any  of  the  following 
errors:  (i)  to  have  mistaken  a  for  the  cause,  when  the 
real  cause  is  r ;  (2)  to  have  mistaken  a  for  the  sole  cause, 
when  a  and  c  are  the  joint  causes,  either  (a)  as  both 
contributing  to  the  total  effect,  or  (/a)  as  being  both  es- 
sential to  the  production  of  any  effect  whatever  ^^  \  (3)  to 
have  mistaken  a  for  the  cause  oi  b^  when  they  are  really 

*^  The  distinction  may  be  illustrated  by  a  familiar  example.  If  a 
cistern  is  tilled  by  two  pipes,  the  water  passing  through  each  cou- 
trilmtcs  to  the  total  amount  of  water  in  the  cistern.  But,  if  the 
cistern  is  t.lled  by  one  pipe  having  two  taps,  one  above  the  other, 
both  taps  must  be  turned  in  order  that  the  cistern  may  receive  any 
water  whatever. 


300 


FALLACIES  INCIDENT 


both  of  them  effects  of  c ;  (4)  to  have  mistaken  a  for 
the  proximate  cause  of  b^  when  it  is  really  only  the  re- 
mote cause,  r,  which  has  escaped  our  attention,  being 
the  proximate  cause. 

To  begin  with  the  latter  class  of  errors. 

(i)  The  following  extract  from  Mr.  Lewes'  Physiology 
of  Common  Life^^  may  serve  as  an  illustration  of  the  first 
subdivision  : — 

'  One  very  general,  indeed  almost  universal,  misconception 
on  this  subject  (asphyxia  or  suffocation)  is  that  carbonic  acid 
is  poisonous  in  the  blood ;  but  the  truth  seems  to  be  that  the 
carbonic  acid  is  noxious  only  when  it  prevents  the  access  of 
oxygen.  There  is  always  carbonic  acid  in  the  blood,  both 
venous  and  arterial.  Its  accumulation  in  the  blood  is  only 
fatal  when  there  is  such  an  accumulation  in  the  atmosphere 
as  will  prevent  its  exhalation  ;  its  mere  presence  in  the  blood 
seems  to  be  quite  harmless,  even  in  large  quantities,  provided 
always  that  it  be  not  retained  there  to  the  exclusion  of 
oxygen.  Carbonic  acid,  when  absorbed  into  the  blood,  which 
is  alkaline,  cannot  there  exert  its  irritant  action  as  an  acid, 
because  it  will  either  be  transformed  into  a  carbonate  or  be 
dissolved.  Bernard  has  injected  large  quantities  into  the 
veins  and  arteries,  and  under  the  skin,  of  rabbits,  and  found 
no  noxious  effect  ensue.  The  more  carbonic  acid  there  is  in 
the  blood,  the  more  will  be  exhaled,  provided  always  that  the 
air  be  not  already  so  charged  with  it  as  to  prevent  this 
exhalation.' 

Here  there  are  really  two  antecedents,  the  presence 
of  carbonic  acid  and  the  exclusion  of  oxygen,  and  the 
noxious  effects,  which  are  erroneously  ascribed  to  the 

*2  Vol.  i.  p.  383. 


TO  INDUCTION, 


301 


former   cause,   ought   properly   to   be   referred    to   the 
latter. 

The  above  extract  exemplifies  this  error  as  vitiating 
an  application  of  the  Method  of  Agreement.  In  the 
following  extracts  from  Dr.  Paris'  Pharmacologia^  it  will 
be  seen  also  to  vitiate  applications  of  the  Method  of 
Difference  : — 


*  Soranus,  who  was  contemporary  with  Galen,  and  wrote 
the  life  of  Hippocrates,  tells  us  that  honey  proved  an  easy 
remedy  for  the  aphthae  of  children ;  but,  instead  of  at  once 
referring  the  fact  to  the  medical  qualities  of  the  honey,  he 
very  gravely  explains  it,  from  its  having  been  taken  from  bees 
that  hived  near  the  tomb  of  Hippocrates  *' ! ' 

*  In  my  life  of  Sir  Humphry  Davy,  I  have  published  an 
anecdote  which  was  communicated  to  me  by  the  late  Mr. 
Coleridge,  and  which  bears  so  strikingly  upon  the  present 
subject  that  I  must  be  excused  for  repeating  it.  As  soon  as 
the  powers  of  nitrons  oxide  were  discovered.  Dr.  Beddoes  at 
once  concluded  that  it  must  necessarily  be  a  specific  for 
paralysis :  a  patient  was  selected  for  the  trial,  and  the 
management  of  it  was  entrusted  to  Davy.  Previous  to  the 
administration  of  the  gas,  he  inserted  a  small  pocket  thermo- 
meter under  the  tongue  of  the  patient,  as  he  was  accustomed 
to  do  upon  such  occasions,  to  ascertain  the  degree  of  animal 
temperature,  with  a  view  to  future  comparison.  The  paralytic 
man,  wholly  ignorant  of  the  nature  of  the  process  to  which 
he  was  to  submit,  but  deeply  impressed,  from  the  representa- 
tions of  Dr.  Beddoes,  with  the  certainty  of  its  success,  no 
sooner  felt  the  thermometer  under  his  tongue,  than  he  con- 
cluded the  talisman  was  in  full  operation,  and  in  a  burst  of 


43 


Pharmacologia,  p.  20. 


302 


FALLACIES  INCIDENT 


enthusiasm  declared  that  he  already  experienced  the  efifect  of 
its  benign  influence  throughout  his  whole  body :  the  oppor- 
tunity was  too  tempting  to  be  lost ;  Davy  cast  an  intelligent 
glance  at  Mr.  Coleridge,  and  desired  his  patient  to  renew  his 
visit  on  the  following  day,  when  the  same  ceremony  was  per- 
formed, and  repeated  every  succeeding  day  for  a  fortnight, 
the  patient  gradually  improving  during  that  period,  when  he 
was  dismissed  as  cured,  no  other  application  having  been 
used*V 

*  Amongst  the  numerous  instances  which  have  been  cited 
to  show  the  power  of  faith  over  disease,  or  of  the  mind  over 
the  bodily  organs,  the  cures  performed  by  royal  touch  have 
been  considered  the  most  extraordinary :  but  it  would 
appear,  upon  the  authority  of  Wiseman,  that  the  cures  which 
were  thus  effected  were  in  reality  produced  by  a  very 
different  cause  ;  for  he  states  that  part  of  the  duty  of  the 
royal  physicians  and  serjeant  surgeons  was  to  select  such 
patients  afflicted  with  scrofula  as  evinced  a  tendency  towards 
recovery,  and  that  they  took  especial  care  to  choose  those 
who  approached  the  age  of  puberty.  In  short,  those  only 
were  produced  whom  Nature  had  shown  a  disposition  to 
cure  ;  and  as  the  touch  of  the  king,  like  the  sympathetic 
powder  of  Digby,  secured  the  patient  from  the  mischievous 
importunities  of  art,  so  were  the  efforts  of  Nature  left  free 
and  uncontrolled,  and  the  cure  of  the  disease  was  not 
retarded  or  opposed  by  the  administration  of  adverse 
remedies.  The  wonderful  cures  of  Valentine  Greatricks, 
performed  in  1666,  which  were  witnessed  by  contemporary 
prelates,  members  of  parliament,  and  fellows  of  the  Royal  So- 
ciety, amongst  whom  was  the  celebrated  Mr.  Boyle,  would  pro- 
bably, upon  investigation,  admit  of  a  similar  explanation.  It 
deser\'es,  however,  to  be  noticed  that,  in  all  records  of  extra- 
ordinary cures  performed   by  mysterious  agents,  there  has 

**  rharmacologia,  p.  28. 


TO  INDUCTION 


?>^?> 


always  been  a  desire  to  conceal  the  remedies  and  other 
curative  means  which  might  have  been  simultaneously  ad- 
ministered. Thus  Oribasius  commends,  in  high  terms,  a 
necklace  of  peony-root  for  the  cure  of  epilepsy  ;  but  we  learn 
that  he  always  took  care  to  accompany  its  use  with  copious 
evacuations,  although  he  assigns  to  them  not  the  least  share 
of  credit  in  the  cure.  In  later  times,  we  have  an  excellent 
specimen  of  this  species  of  deception,  presented  to  us  in  a 
work  on  scrofula  by  Mr.  Morley,  written,  as  we  were  in- 
formed, for  the  sole  purpose  of  restoring  the  much-injured 
character  and  use  of  the  vervain;  in  which  the  author 
directs  the  root  of  that  plant  to  be  tied  with  a  yard  of  white 
satin  ridand  a.round  the  neck  ;— but  mark— during  the  period 
of  its  application,  he  calls  to  his  aid  the  most  active  medi- 
cines in  the  materia  medica.  "  It  is  unquestionable,"  says 
Voltaire,  speaking  of  sorceries,  "that  certain  words  and 
ceremonies  will  effectually  destroy  a  flock  of  sheep,  if  ad- 
ministered with  a  sufficient  portion  of  arsenic  *V" 

*  Our  inability  upon  all  occasions  to  appreciate  the  efforts 
of  nature,  in  the  cure  of  disease,  must  necessarily  render  our 
notions,  with  respect  to  the  powers  of  art,  liable  to  numerous 
errors  and  deceptions.  Hence  protracted  or  wire-drawn 
cures  ought  to  be  very  cautiously  received  as  evidences  of  the 
success  of  medical  treatment.  Many  diseases  require  only 
time  to  enable  nature  to  remove  them.  All  the  long  train 
connected  with  hysteria  are  cured  by  time;  the  solution  of 
which,  as  Mr.  Travers  has  observed,  is  to  be  found  in  the 
fact  that  the  hysteric  period  wanes,  and  the  restlessness 
of  the  temperament  undergoes  a  slow  but  salutary  change. 
Nothing,  certainly,  is  more  natural,  although  it  may  be  very 
erroneous,  than  to  attribute  the  cure  of  a  disease  to  the  last 
medicine  that  had  been  administered ;  the  advocates  even  of 
amulets  and  charms  have  been  thus   enabled  to  appeal  to 

**  Pharmacologia,  p.  30. 


304 


FALLACIES  INCIDENT 


the  testimony  of  what  they  call  experience,  in  justification  of 
their  superstition  *V 

Of  a  similar  character  was  the  old  superstition,  noticed 
by  Sir  Thomas  Browne  *'  and  many  other  authors,  that 
the  hardest  stone  could  be  broken  by  goat's  blood :  — 

*  And,  first,  we  hear  it  in  every  mouth,  and  in  many  good 
authors  read  it,  that  a  diamond,  which  is  the  hardest  of 
stones,  not  yielding  unto  steel,  emery,  or  any  thing  but  its 
own  powder,  is  yet  made  soft,  or  broke  by  the  blood  of  a 

goat But   this,  I  perceive,  is  easier  affirmed  than 

proved.  For  lapidaries,  and  such  as  profess  the  art  of  cuttin^^ 
this  stone,  do  generally  deny  it;  and  they  that  seem  to 
countenance  it  have  in  their  deliveries  so  qualified  it,  that 
little  from  thence  of  moment  can  be  inferred  for  it.  For 
first,  the  holy  fiithers,  without  a  further  enquir>%  did  take  it 
for  granted,  and  rested  upon  the  authority  of  the  first  de- 
liverers. .  .  .  But  the  words  of  Pliny,  from  whom  most  likely 
the  rest  at  first  derived  it,  if  strictly  considered,  do  rather 
overthrow,  than  any  way  advantage  this  effect.  His  words 
are  these :  Hirchio  riimpitur  sanguine^  nee  aliter  quani 
recenti  calidoqiie  macerata,  et  sic  quoque  imtltis  ictibus^  tunc 
etiam  prcpterquam  eximias  incudes  malleosque  ferreos  fran- 
gens.  That  is,  it  is  broken  with  goat's  blood,  but  not  except 
it  be  fresh  and  warm,  and  that  not  without  many  blows,  and 
then  also  it  will  break  the  best  anvils  and  hammers  of  iron.' 

The  example  of  Sir  Kenelm  Digby's  sympathetic 
powder  (already  quoted  pp.  270-1)  also  illustrates  this 
class  of  fallacies  *^ 

**  Pharmacologia^  p.  88. 

•^  Enquiry  into  Vulgar  and  Common  Errors,  Bk.  II.  ch.  v.  Col- 
lected Works,  vol.  ii.  pp.  334,  335. 

•*  These  instances,   together  with  many  others  in  this  chapter, 


TO  INDUCTION. 


3<=>S 


It  should  be  noticed  that,  when  we  attribute  a  pheno- 
menon to  a  wrong  cause,  it  does  not  always  follow  that 
this  cause,  had  it  been  in  action,  might  not  have  pro- 
duced the  event.  Thus,  we  may  wrongly  attribute  death 
in  some  given  case  to  poison,  or  infection  to  actual 
contact  with  a  diseased  person,  or  ignition  to  friction, 
because  these  causes  were  not  then  and  there  in  action, 
though,  had  they  been  actually  operating,  they  would 
have  been  perfectly  competent  to  produce  the  effect. 
When  we  make  a  mistake  of  this  kind,  it  frequently  arises 
from  our  concentrating  our  attention  exclusively  on  some 
one  or  a  few  of  the  possible  causes  which  may  produce 
a  given  effect,  thus  neglecting  the  consideration  of  the 
Plurality  of  Causes,  to  which  attention  has  repeatedly 
been  drawn  in  the  previous  pages*'. 

(2)  When  an  effect  is  the  joint  result  of  two  or  more 

illustrate  the  ancient  fallacies  *  Non  causa  pro  causa,'  and  '  Post  hoc, 
ergo  propter  hoc'  It  will  probably  have  already  occurred  to  the 
student  that  some  of  the  examples  just  cited  might  have  been  equally 
well  adduced  as  examples  of  the  fallacy  of  non-observation.  It,  in 
fact,  frequently  happens  that  the  same  error  may  be  assigned  indif- 
ferently to  two  or  more  sources  of  deception.  '  From  the  elliptical 
form,'  says  Archbishop  Whately  {Elements  of  Logic ,  Bk.  iii.  §1), 
*  in  which  all  reasoning  is  usually  expressed,  and  the  peculiarly 
involved  and  oblique  form  in  which  fallacy  is  for  the  most  part 
conveyed,  it  must  of  course  be  often  a  matter  of  doubt,  or  rather  of 
arbitrary  choice,  not  only  to  which  genus  each  kind  of  fallacy  should 
be  referred,  but  even  to  which  kind  to  refer  any  one  individual 
fallacy.'  Thus,  so  intimately  are  our  intellectual  operations  blended, 
that  it  is  often  extremely  difficult  to  decide  whether  a  mistake  be 
mainly  due  to  defective  observation  or  erroneous  reasoning. 
♦»  See  pp.  6,  23,  127-8,  131-4. 


3o6 


FALLACIES  INCIDENT 


causes,  the  causes  may  either  simply  contribute  towards 
the  production  of  the  total  result,  though  one  only  would 
produce  some  portion  of  it,  or  they  may  all  be  essential 
to  the  production  of  any  result  whatever.  It  would  be 
convenient  if,  in  the  former  case,  we  could  speak  of  the 
causes  asyW«/  causes,  in  the  latter  asyW/?/  conditions,  but 
to  do  so  would  perhaps  be  too  great  an  innovation  on 
established  language. 

(a)  An  instance  of  supposing  that  a  phenomenon  is 
entirely  due  to  one  cause,  when  it  seems  in  reality  to 
be  only  partially  due  to  it,  is  furnished  by  the  prevalent 
notion  that  the  heart  is  the  sole  cause  of  the  circulation 
of  the  blood. 

*  What  is  it,'  says  Mr.  Lewes  '^  '  which  causes  the  blood  to 
circulate?  "The  heart,"  answers  an  unhesitating  reader. 
That  the  heart  pumps  blood  incessantly  into  the  arteries,  and 
that  this  pumping  must  drive  the  stream  onwards  with  great 
force,  there  is  no  doubt ;  but,  although  the  most  powerful 
agent  in  the  circulation,  the  heart  is  not  the  sole  agent ;  and 
the  more  we  study  this  difficult  question,  the  more  our 
doubts  gather  round  the  explanation.' 

*  Let  a  few  of  the  difficulties  be  stated.  There  have  been 
cases  of  men  and  animals  born  without  a  heart :  these  "  acar- 
diac  monsters  "  did  not  live,  indeed  could  not  live;  but  they 
had  grown  and  developed  in  the  womb,  and  consequently 
their  blood  must  have  circulated.  In  most  of  these  cases 
there  has  been  a  twin  embryo,  which  was  perfect ;  and  the 
circulation  in  both  was  formerly  attributed  to  the  heart  of 
the  one  ;  but  it  has  been  fully  established  that  this  is  not  the 
case.     Further,  Dr.  Carpenter  reminds  us  that  "  it  has  occa- 

^  Physiology  of  Common  Life,  vol.  i.  p.  3^2. 


TO  INDUCTION. 


307 


sionally  been  noticed  that  a  degeneration  in  the  structure  of 
the  heart  has  taken  place,  during  life,  to  such  an  extent  that 
scarcely  any  muscular  tissue  could  at  last  be  detected  in  it, 
but  without  any  such  interruption  to  the  circulation  as  must 
have  been  anticipated  if  this  organ  furnishes  the  sole  im- 
pelling force."  On  the  other  hand,  an  influence  acting  on 
the  capillaries  will  give  a  complete  check  to  the  action  of  the 
heart,  although  that  organ  is  itself  perfectly  healthy  and 
vigorous.' 

Mr.  Lewes  then  proceeds  to  discuss  the  subject  at 
greater  length,  but  the  above  quotation  is  sufficient  for 
my  purpose. 

A  familiar  instance  of  this  error  occurs  in  the  vulgar 
notion  that  the  mean  annual  temperature  of  a  place  is 
exclusively  determined  by  its  latitude.  The  reader  need 
hardly  be  told  that  in  this  case  there  are  many  other 
causes  at  work,  namely,  elevation,  distance  from  the  sea, 
proximity  of  mountain  chains,  and  the  like. 

When  a  number  of  causes  contribute  towards  the  total 
effect,  it  is  plain  that,  as  in  the  last  instance,  they  may 
operate  in  the  way  of  modifying,  counteracting,  or  even 
frustrating''^  each  other's  influence.  This  is  a  considera- 
tion which  it  is  often  of  the  utmost  importance  to  bear 
in  mind,  as  will  be  obvious  from  the  following  examples, 
extracted,  the  former  from  Dr.  Paris'  Pharmacologia  ■■'^, 
the  latter  from  Sir  G.  C.  Lewis'  Methods  of  Observation 
and  Reasoning  in  Politics  ^\ 

•^^  We  sometimes  speak  of  causes  '  wholly  or  partially  counter- 
acting each  other.'  It  would  be  an  advantage  if  we  could  appro- 
priate the  \sQxiS.  frustration  to  express  complete  counteraction. 

^>  P.  498.  '^  Vol.  i.  p.  386. 

X  2 


3o8 


FALLACIES  INCIDENT 


*  In  ordering  saline  draughts  as  vehicles  for  active  medi- 
cines, it  is  very  important  that  they  should  be  rendered 
perfectly  neutral ;  the  effect  of  a  predominating  acid  or  alkali 
may  produce  decompositions  fatal  to  the  efficacy  of  the 
remedy,  as  the  practitioner  will  fully  understand  by  a  refer- 
ence to  the  Acetate  of  Ammonia  and  other  preparations  in 
the  Table  of  Incompatibles.  In  prescribing  them  to  be 
taken  in  a  state  of  effervescence,  we  must  consider  whether 
the  disengaged  carbonic  acid  may  not  invalidate  the  powers 
of  the  remedies  simuhaneously  given  with  them.  I  should 
certainly  recommend  such  a  form  to  be  avoided,  in  all  cases 
where  a  salt  of  lead  had  been  administered,  for  the  carbomc 
acid  retained  in  the  stomach  might  probably  convert  it  into 
k  carbonated 

*  But  it  is  to  be  borne  in  mind  that,  in  estimating  negative 
instances,  due  allowance  must  be  made  for  the  occasional 

frustration   of  causes For   example  :  it   might   be 

argued,  from  the  occurrence  of  several  cases  in  which  the 
absence  of  high  import  duties  and  of  commercial  restrictions 
was   accompanied  with    abundance  and  cheapness  of  com- 
modities, that  the  former  was  the  cause  of  the  latter.  Certain 
instances  might  then  occur,  in  which  the  former  existed  with- 
out  the  latter ;  but  each  of  these  exceptional  cases  might 
be  accounted  for,  by  showing  that  there  was  a  special  circum- 
stance, such  as  a  deficient  supply,  or  interruption  of  inter- 
course by  war  or  blockade,  which  partially  obstructed,  and  for 
a  time  suspended,  the  operation  of  the  former  cause.     Again : 
it  might  be  shown,  by  the  evidence  of  facts,  that  the  operation 
of  a  new  law  had  been  generally  beneficial,  with  the  exception 
of  certain  districts,  where  its   enforcement  had   been  pre- 
vented or  retarded  by  certain  peculiar  and  accidental  circum- 
stances. Exceptions  of  this  kind,  which  admit  of  an  adequate 
special    explanation,  serve   rather   to   confirm   the    general 
inference  than  to  weaken  it ;  inasmuch  as  they  raise  the  pre- 


TO  INDUCTION, 


309 


sumption  that,  but  for  the  partial  obstruction  to  the  cause,  it 
would  have  operated  in  these  as  in  the  other  instances  where 
no  obstructions  existed^*.' 

'  It  is  probably  from  observing  this  case  of  the  problem 
of  causation,  that  the  popular  error  has  arisen  of  supposing 
that  a  rule  is  sometimes  proved  by  its  exceptions.  Every 
exception  to  a  general  proposition  must,  in  so  far  as  it  is  an 
exception,  detract  from  the  application  of  the  proposition,  and 
consequently  disprove  [or  rather  go  towards  disproving]  il. 
Thus,  if  it  were  asserted  that  all  cloven-footed  animals 
ruminate,  this  assertion  certainly  would  receive  no  confirma- 
tion from  the  fact,  that  certain  cloven-footed  animals— such 
as  the  hog— do  not  ruminate.  If,  however,  the  exception,  as 
in  the  case  which  we  have  been  examining,  admitted  of  a 
peculiar  explanation,  and  it  could  be  shown  that  the  tiisus  or 
tendency  of  the  cause  was  the  same  in  the  exceptional  as  in 
the  other  instances,  but  that  in  the  former  it  was  counteracted 
and  overcome,  while  in  the  latter  it  was  not — then  the 
exception  may  be  said  not  to  invalidate,  but  rather  to  confirm 
the  rule.' 


The  above  passage  is  noteworthy,  as  furnishing  a  good 
comment  on  the  maxim,  Exceptio  probat  regulam^  a 
maxim  which  is,  of  course,  only  applicable  where  the 
exceptions  are  apparent,  and  where  they  admit  of  ex- 
planation in  conformity  with  the  rule. 

(3)  That  every  event  depends  upon  the  concurrence 
of  a  number  of  causes,  positive  and  negative,  or,  as  they 
are  often  called,  conditions,  has  already  been  pointed 
out  (Chap.  I.  pp.  13-16).     Thus,  the  burning  of  a  fire 

**  Sir  G.  C.   Lewis'  Methods  of  Observation  ami  Reasoning  in 
Politics t  vol.  i.  p.  386. 


310  FALLACIES  INCIDENT 

depends  not  only  on  the  application  of  a  lighted  match 
and   the  supply  of  fuel,  but  also  on  the  presence  of 
atmospheric  air,  or  rather  of  the  oxygen  which  it  con- 
tains, though,  from  the  universal  presence  of  air,  we  are 
less  apt  to  think  of  the  latter  cause  than  of  the  former 
ones.     The  importance,  however,  of  not  overlooking  this 
consideration  is  shown  by  the  extent  to  which  we  can 
augment  the  temperature   by  constantly  bringmg  fresh 
currents  of  air  into  contact  with  any  heated  mass,  as  well 
as  by  the  similar  and  familiar  phenomenon  of  the  in- 
creased brightness  with  which  a  fire  burns  on  a  frosty 
day,  owing  to  the  better  draught. 

The  importance  of  bearing  in   mind  that  an  event 
depends  upon  a  concurrence  of  causes  may  be  further 
illustrated  by  the  boiling-point  of  water.     The  point  at 
which  water  (by  which  I  mean  pure  water)  boils  depends 
slightly  on  the  nature  of  the  vessel,  but  mainly  upon  two 
causes  or  conditions,  the  temperature  of  the  water  and 
the   pressure   of  the   atmosphere.      Now,  as  the  latter 
varies   at   different   heights   and   in   different   states   of 
weather,  water  does  not  always  boil  at  the  same  tempera- 
ture, the  boiling-point  being,  as  a  rule,  diminished  by  i 
for  every  590  feet  that  we  ascend,  so  that,  whereas  at  the 
sea  level  water  boils  at  about  212°  Fahrenheit,  on  the 
top  of  Mont  Blanc  it  boils  at  about  185  .     It  is  obvious 
that  any  one,  not  bearing  in  mind  this  fact,  might  be 
exposed  to  the  greatest  practical  inconveniences. 

The  following  quotations  from  Dr.   Paris'  Pharmaco- 
lona  will  furnish  a  sufficient  illustration  of  the  importance 


TO  INDUCTION 


311 


of  this  consideration  and  of  the  errors  which  may  result 
from  neglecting  it. 

'  In  some  cases  of  irritability  of  stomach,  the  addition  of  a 
small  quantity  of  opium  will  impart  efficacy  to  a  remedy 
otherwise  inert ;  an  emetic  will  often  thus  be  rendered  more 
active,  as  I  have  frequently  witnessed  in  my  practice.  In 
some  states  of  mania,  and  affections  of  the  brain,  emetics  will 
wholly  fail,  unless  the  stomach  be  previously  influenced  and 
prepared  by  a  narcotic.  I  have  often  also  found  that  the 
system  has  been  rendered  more  susceptible  of  the  influence 
of  mercury  by  its  combination  with  antimony  and  opium. 
So,  again,  when  the  system  is  in  that  condition  which  is 
indicated  by  a  hot  and  dry  skin,  squill  will  fail  in  exciting 
expectoration;  but  administer  it  in  conjunction  with  am- 
monia, and  in  some  cases  with  Antimonial  Wine  and  a 
saline  draught,  and  its  operation  will  be  promoted.  As  a 
diuretic.  Squill  is  by  no  means  active,  when  singly  ad- 
ministered, but  Calomel,  or  some  mercurial,  when  in  com- 
bination with  it,  appears  to  direct  its  influence  to  the  kidneys, 
and  in  some  unknown  manner  to  render  these  organs  more 
susceptible  of  its  influence  *\' 

*  It  has  been  determined  by  the  most  ample  experience 
that  substances  will  produce  effects  upon  the  living  system, 
when  presented  in  a  state  of  simple  mechanical  mixture,  very 
different  from  those  which  the  same  medicinal  ingredients 
will  occasion  when  they  are  combined  by  the  agency  of 
chemical  affinity.  To  illustrate  this  by  a  simple  case,— a 
body  suspended  in  a  mixture  in  the  form  of  a  powder,  will 
act  ver>'  differently  if  held  in  solution  by  a  fluid.  The  relative 
effects  of  alcohol  in  the  form  of  what  is  termed  "  spirit,''  and 
in  that  of  wine,  may  be  explained  upon  the  same  principle ; 
in  the  former  case  it  is  in  a  state  of  mixture,  in  the  latter  in 

*^  I*Jiarmacologia,  p.  388. 


31  a 


FALLACIES  INCIDENT 


that  of  combination.  It  has  been  demonstrated,  beyond  all 
doubt,  that  a  bottle  of  port,  madeira,  or  sherry,  actually  con- 
tains as  much  alcohol  as  exists  in  a  pint  of  brandy ;  and  yet 
how  different  the  effect  !-a  fact  which  affords  a  very  strikmg 
illustration  of  the  extraordinary  powers  of  chemical  combma- 
tion  in  modifying  the  activity  of  substances  upon  the  living 
system  ^^: 

*  It   has   been  very  generally  supposed  that   substances, 
whose  application  does  not  produce  any  sensible  action  upon 
the  healthy  system,  cannot  possess  medicinal  energy ;  and, 
on  the  contrary,  that  those  which  occasion  an  obvious  effect 
must  necessarily  prove  active  in  the  cure  or  palliation  of 
disease.     To  this  general  proposition,  under  certain  limita- 
tions and  restrictions,  we  may  perhaps  venture  to  yield  our 
assent  ;  but  it  cannot  be  too  early,  nor  too  forcibly  impressed 
upon  the  mind  of  the  young  practitioner,  that  medicines  are, 
for  the  most  part,  but  relative  agents,  producing  their  effects 
in  reference  only  to  the  state  of  the  living  frame.     We  must, 
therefore,  concur  with  Sir  Gilbert  Blane  in  stating  that  the 
virtues  of  medicines  cannot  be  fairly  essayed,  nor  beneticially 
ascertained,  by  trying  their  effects  on  sound  subjects,  because 
that  particular  morbid  condition  does  not  exist  which  they 
may  be  exclusively  calculated  to  remove ;  thus,  in  a  robust 
state  of  the  body,  the  effects  of  steel,  in  commendation  of 
which,  in  certain  diseases,  professional  opinion  is  unanimous, 
may  be  wholly  imperceptible.     Bitter  tonics,  also,  may  either 
prove  entirely  inert,  or  they  may  give   strength,  relax  the 
bowels,  or  induce  constipation,  according  to  the  particular 
condition  of  the  patient  to  whom  they  are  administered  ;  so 
again,  in  a  healthy  state  of  the  stomach,  a  few  grains  of  soda 
or  magnesia  will  not  occasion  the  least  sensible  effect,  but, 
where  that  organ  is  infested  with  a  morbid  acid,  immediate 
relief  will  follow  the  ingestion  of  the  one,  and  purgation  that 

"  Pharmacologia,  pp.  426,  427. 


TO  INDUCTION 


zn 


of  the  other.  By  not  reasoning  upon  such  facts,  physicians 
have,  in  my  opinion,  very  unphilosophically  advanced  to 
conclusions  respecting  the  inefficacy  of  certain  agents.  They 
have  administered  particular  preparations  in  large  doses, 
and,  not  having  observed  any  visible  effects,  have  at  once 
denounced  them  as  inert.  I  might  allude,  for  instance,  to  the 
tris-nitrate  ofbisjnuth,  a  substance  which,  however  powerless 
in  health,  I  am  well  satisfied,  from  ample  experience,  is 
highly  efficacious  in  controUing  certain  morbid  states  of  the 
stomach.  Dr.  Robertson  has  well  observed  that  disease  calls 
forth  the  powers,  and  modifies  the  influence  of  medicines. 
That  which  agitates  the  calm  of  health  may  soothe  the  irri- 
tation of  illness,  and  that,  which  without  opposition  is  inert, 
may  act  powerfully  where  it  meets  with  an  opponent.  Ex- 
periments should  be  made  on  the  sick,  in  order  to  determine 
how  the  sick  will  be  affected,  and  nothing  should  be  pro- 
nounced feeble,  merely  because  it  has  done  nothing  where 
there  was  nothing  to  be  done'^'.' 

To  adduce  one  more  illustration :  insanity,  though 
sometimes  due  to  a  number  of  causes,  each  one  of 
which  simply  contributes  to  and  augments  the  affection, 
which  would  still  exist,  though  in  a  weaker  degree,  even 
if  some  of  them  were  absent,  appears  at  other  times  to 
be  the  joint  result  of  a  number  of  causes,  the  presence 
of  every  one  of  which  seems  to  be  essential  to  the  pro- 
duction of  any  effect  so  definite  as  to  deserve  the  name 
of  mental  derangement.  The  train,  in  these  cases,  appears 
to  be  laid  by  a  number  of  precedent  circumstances,  and 
the  addition  of  some  one  other  circumstance  seems  to  be 
the  spark  which  produces  the  conflagration. 

*"  Pharmacologia,  pp.  133,  134. 


3^4 


FALLACIES  INCIDENT 


*  When  we  are  told,'  says  Dr.  Maudsley  »^  *that  a  man  has 
become  deranged  from  anxiety  or  grief,  we  have  learned  very 
little  if  we  rest  content  with  that.     How  does  it  happen  that 
another  man,  subjected  to  an  exactly  similar  cause  of  grief, 
does  not  go  mad  ?    It  is  certain  that  the  entire  causes  cannot 
be  the  same  where  the  effects  are  so  different ;  and  what  we 
want   to   have   laid  bare  is  the   conspiracy  of  conditions, 
internal  and  external,  by  which  a  mental  shock,  inoperative 
in  one  case,  has  had  such  serious  consequences  in  another. 
A  complete  biographical  account  of  the  individual,  not  neg- 
lecting the  consideration  of  his  hereditary  antecedents,  would 
alone  suffice   to   set  forth   distinctly  the   causation   of  his 
insanity.     If  all  the   circumstances,  internal  and   external, 
were  duly  scanned  and  weighed,  it  would  be  found  that  there 
is  no  accident  in  madness  ;  the  disease,  whatever  form  it 
might   take,  by  whatsoever   complex   concurrence   of  con- 
ditions, or  by  how  many  successive  links  of  causation,  it 
might  be  generated,  would  be  traceable  as  the   inevitable 
consequence  of  certain  antecedents,  as  plainly  as  the  ex- 
plosion of  gunpowder  may  be  traced  to  its  causes,  whether 
the  train  of  events  of  which  it  is  the  issue  be  long  or  short. 
The  germs  of  insanity  are  sometimes  latent  in  the  founda- 
tions of  the  character,  and  the  final  outbreak  is  perhaps  the 
explosion  of  a  long  train  of  antecedent  preparations.' 

(3)  The  phenomena  of  insanity  also  furnish  a  good 
illustration  of  the  next  source  of  error,  the  mistaking  of 
joint  effects  for  cause  and  effect.  In  this,  as  in  many 
other  diseases,  symptoms  are  often  mistaken  for  causes. 
Thus,  it  is  not  uncommon  to  hear  violent  religious  ex- 
citement or  inordinate  grief  adduced  as  causes  of 
insanity,  whereas  these   are  probably  merely  incipient 

^  Physiology  and  Pathology  of  Mitid,  Part  II.  ch.  i.  p.  225. 


TO   INDUCTION 


Z^S 


symptoms,  due,  in  the  vast  majority  of  cases,  to  precisely 
the  same  combination  of  physical  and  mental  causes, 
which,  when  they  operate  with  greater  intensity,  ulti- 
mately issue  in  definite  and  unmistakable  insanity. 

We  have  an  instructive  instance  of  the  same  error  in 
some  of  the  speculations  respecting  the  origin  of  fevers. 
In  Abdominal  Typhus  (the  so-called  Typhoid  or  Enteric 
Fever  of  the  English  Physicians)  the  febrile  symptoms 
(Pyrexia,  Erethism,  &c.)  have  been  ascribed  to  certain 
lesions  of  the  glandular  structures  of  the  intestines ;  but 
a  wider  observation  has  shown  that  the  other  symptoms 
often  precede  by  some  time  the  formation  of  the  lesions, 
and  that  the  fever  may  even  run  a  fatal  course,  though 
it  may  be  impossible,  in  a  post-mortem  examination,  to 
detect  the  specific  lesions  in  question.     Practically,  the 
correction  of  this  and  similar  errors  is  of  great  import- 
ance, as  much  mischief  may  be  done,  and  much  time 
may  be  lost,  by  a  mode  of  treatment  which,  through 
mistaking  symptoms  for  causes,  or  co-effects  for  cause 
and  effect,  addresses  itself  only  to  the  consequences  of 
the  malady,  and  leaves  the  real  source  of  evil  unattacked. 

The  following  anecdote,  told  by  Dr.  Paris,  affords  an 
amusing  illustration  of  the  extent  to  which  the  ignorant, 
in  reasoning  on  cause  and  effect,  may  be  deceived  by  an 
invariable,  or  even  frequent,  concurrence  of  events. 

*  It  should,'  says  he•^  'be  kept  in  mind,  that  two  events 
may  arise  from  a  common  cause,  and  be  co-existent,  and  yet 
have  not  the  most  remote  analogy  to,  or  dependence  upon, 

'*'•'  Pharmacologia,  p.  89. 


3i6 


FALLACIES  INCIDENT 


each  other.  It  was  a  general  belief  at  St.  Kilda,  that  the 
arrival  of  a  ship  gave  all  the  inhabitants  colds.  Dr.  John 
Campbell  took  a  great  deal  of  pains  to  ascertain  the  fact,  and 
to  explain  it  as  the  effect  of  effluvia  arising  from  human 
bodies ;  the  simple  truth,  however,  was  that  the  situation  of 
St.  Kilda  renders  a  north-east  wind  indispensably  necessary 
before  a  stranger  can  land,— the  wind,  not  the  stranger, 
occasioned  the  epidemic' 

In  speculations  on  the  history  of  language,  languages, 
which  recent  investigation  has  shown  to  be  related  col- 
laterally, were  by  older  philologists  erroneously  regarded 
as  standing  to  each  other  in  the  relation  of  parent  and 
child.  I  extract  from  Professor  Max  Miiller^s  Lectures  on 
the  Science  of  Language'''  the  following  illustration,  which 
will  already  be  familiar  to  many  of  my  readers  :— 

*  A  glance  at  the  modern  history  of  language  will  make 
this  clearer.  There  never  could  be  any  doubt  that  the 
so-called  Romance  languages,  Italian,  Wallachian,  Pro- 
vencjar",  French,  Spanish,  and  Portuguese,  were  closely 
related  to  each  other.  Everybody  could  see  that  they  were 
all  derived  from  Latin.  But  one  of  the  most  distinguished 
French  scholars,  Raynouard,  who  has  done  more  for  the 
history  of  the  Romance  languages  and  literature  than  any 
one  else,  maintained  that  Provencal  only  was  the  daughter  of 
Latin  ;  whereas  French,  Italian,  Spanish, and  Portuguese  were 

•"  First  Series.     Lecture  V. 

«i  The  exact  relationship  of  French  to  Provencal  may  be  repre- 
sented thus:  the  Peasant  Latin  became  in  the  South  of  France  the 
Langue  d'Oc  (or  Proven9al),  and  in  the  North  the  Langue  d'Oil,  of 
which  the  French  (or  the  dialect  of  the  Isle  de  France^  was  the 
principal  dialect,  and  has  in  its  modern  form  become  the  language 
of  the  nation.  Scj  Brachet's  Historical  Grammar  (Dr.  Kitchin's 
Translation\  p.  i8;  7th  ed.  pp.  2J-3. 


TO   INDUCTION, 


317 


the  daughters  of  Provencal.  He  maintained  that  Latin  passed, 
from  the  seventh  to  the  ninth  century,  through  an  inter- 
mediate stage,  which  he  called  Langue  Romane,  and  which  he 
endeavoured  to  prove  was  the  same  as  the  Provengal  of 
Southern  France,  the  language  of  the  Troubadours.  Ac- 
cording to  him,  it  was  only  after  Latin  had  passed  through 
this  uniform  metamorphosis,  represented  by  the  Langue 
Romane  or  Provencal,  that  it  became  broken  up  into  the 
various  Romance  dialects  of  Italy,  France,  Spain,  and 
Portugal.  This  theory,  which  was  vigorously  attacked  by 
August  Wilhelm  von  Schlegel,  and  afterwards  minutely 
criticised  by  Sir  Cornewall  Lewis,  can  only  be  refuted  by  a 
comparison  of  the  Provencal  grammar  with  that  of  the  other 
Romance  dialects.  And  here,  if  you  take  the  auxiliary  verb 
to  be,  and  compare  its  forms  in  Provengal  and  French,  you 
will  see  at  once  that,  on  several  points,  French  has  presei-ved 
the  original  Latin  forms  in  a  more  primitive  state  than  Pro- 
vencal, and  that,  therefore,  it  is  impossible  to  classify  French 
as  the  daughter  of  Provengal,  and  as  the  granddaughter 
of  Latin.     We  have  in  Provencal  :  — 

sem,  corresponding  to  the  French  nous  som?nes, 
etz  „  vous  t'tes, 

son  „  its  sont. 


and  it  would  be  a  grammatical  miracle  if  crippled  forms, 
such  as  sefn,  etz,  and  son,  had  been  changed  back  again  into 
the  more  healthy,  more  primitive,  more  Latin,  sommes,  etes, 
sont ;  sumus,  estis,  sunt. 

Let  us  apply  the  same  test  to  Sanskrit,  Greek,  and  Latin  : 
and  we  shall  see  how  their  mutual  genealogical  position 
is  equally  determined  by  a  comparison  of  their  grammatical 
forms.  It  is  as  impossible  to  derive  Latin  from  Greek,  or 
Greek  from  Sanskrit,  as  it  is  to  treat  French  as  a  modifica- 
tion of  Provencal.  Keeping  to  the  auxiliary  verb  to  be,  we 
find  that  I  am  is  in 


3i8 


FALLACIES  INCIDENT 


Sanskrit 
as  mi 


Greek 
esmi 


Lithuanian 
esmi. 


The  root  is  as,  the  termination  mi. 

Now,  the  termination  of  the  second  person  is  si,  which, 
together  with  as,  or  es,  would  make 


as-st 


es-si 


es-st. 


But  here  Sanskrit,  as  far  back  as  its  history  can  be  traced, 
has  reduced  assi  to  asi ;  and  it  would  be  impossible  to 
suppose  that  the  perfect,  or,  as  they  are  sometimes  called, 
organic,  forms  in  Greek  and  Lithuanian,  cs-si,  could  first 
ha^'ve  passed  through  the  mutilated  state  of  the  Sanskrit  asi. 

The  third  person  is  the  same  in  Sanskrit,  Greek,  and 
Lithuanian,  as-/i  or  es-W;  and,  with  the  loss  of  the  final  /, 
we  recognise  the  Latin  esi,  Gothic  is^,  and  Russian  csl\ 

The  same  auxiliary  verb  can  be  made  to  furnish  sufficient 
proof  that  Latin  never  could  have  passed  through  the  Greek, 
or  what  used  to  be  called  the  Pelasgic  stage,  but  that  both 
are  independent  modifications  of  the  same  original  language. 
In  the  singular,  Latin  is  less  primitive  than  Greek ;  for  sum 
stands  for    es-iim,  es   for   es-is,  est  for  es-ii.     In   the   first 
person   plural,  too,   sumus  stands  for  es-umus,  the   Greek 
cs-mcs,  the   Sanskrit  's?nas.     The    second    person    es-'tis   is 
equal  to  (ireek  es-te,  and  more  primitive  than  Sanskrit  stha. 
But  in  the  third  person  plural  Latin  is  more  primitive  than 
Greek.     The  regular  form  would  be  as-atiii;  this,  in  Sans- 
krit, is  changed  into  santi.   In  Greek,  the  initial  s  is  dropped, 
and  the  yKolic  enti  is  finally  reduced  to  eisi.     The  Latin,  on 
the  contrary,  has  kept  the  radical  s,  and  it  would  be  perfectly 
impossible  to  derive  the  Latin  sunt  from  the  Greek  eisi! 

(4)  A  not  uncommon  source  of  error  is  the  confusion 
of  the  proximate  with  the  primary  or  remote  cause  of  a 
phenomenon.  To  be  on  our  guard  against  this  error  is 
often  of  the  utmost  practical  importance  :  for  the  removal 


TO  INDUCTION. 


319 


of  the  proximate  cause  may  only  temporarily  remove  the 
effect,  and  the  primary  cause  may,  after  a  time,  repro- 
duce it ;  or,  again,  the  removal  of  the  primary  cause  may 
still  leave  the  proximate  cause  in  full  action.  This  error 
is  well  exemplified  in  Mr.  Lewes'  account  of  Thirst. 


'  The  sensation  of  Thirst  is  not  merely  a  sensation  depen- 
dent on  a  deficiency  of  liquid  in  the  system,  but  a  local  sensa- 
tion dependent  on  a  local  disturbance  :  the  more  water  these 
men  (the  prisoners  confined  in  the  Black  Hole  at  Calcutta) 
drank,  the  more  dreadful  seemed  their  thirst  ;  and  the  mere 
sight  of  water  rendered  the  sensation,  which  before  was 
endurable,  quite  intolerable.  The  increase  of  the  sensation 
following  a  supply  of  water,  would  be  wholly  inexplicable  to 
those  who  maintain  that  the  proximate  cause  of  Thirst  is 
deficiency  of  liquid  ;  but  is  not  wholly  inexplicable,  if  we 
regard  the  deficiency  as  the  primary,  not  the  proximate 
cause  :  for  this  primary  cause  having  set  up  a  feverish  con- 
dition in  the  mouth  and  throat,  that  condition  would  con- 
tinue after  the  original  cause  had  ceased  to  exist.  The 
stimulus  of  cold  water  is  only  a  momentary  relief  in  this  case, 
and  exaggerates  the  sensation  by  stimulating  a  greater  flow 
of  blood  to  the  parts.  If,  instead  of  cold  water,  a  little  luke- 
warm tea,  or  milk-and-water,  had  been  drunk,  permanent 
relief  would  have  been  attained  ;  or  if,  instead  of  cold  water, 
a  lump  of  ice  had  been  taken  into  the  mouth,  and  allowed  to 
melt  there,  the  effect  would  have  been  very  different — a  tran- 
sitory application  of  cold  increasing  the  flow  of  blood,  a 
continuous  application  driving  it  away. 

*  We  must  not,  however,  forget  that,  although,  where  a 
deficiency  of  liquid  has  occasioned  a  feverish  condition  of 
the  mouth  and  throat,  no  supply  of  cold  liquid  will  at  once 
remove  that  condition,  the  relief  of  the  Systemic  sensation 
not  immediately  producing  relief  of  the  local  sensation,  never- 


320 


FALLACIES  INCIDES'T 


theless,  so  long  as  the  system  is  in  need  of  liquid,  the  feeling 
of  thirst  must  continue.  Claude  Bernard  observed  that  a  dog 
which  had  an  opening  in  its  stomach  drank  unceasingly 
because  the  water  ran  out  as  fast  as  it  was  swallowed  ;  in 
vain  the  water  moistened  mouth  and  throat  on  its  way  to  the 
stomach.  Thirst  was  not  appeased  because  the  water  was 
not  absorbed.  The  dog  drank  till  fatigue  forced  it  to  pause, 
and  a  few  minutes  afterwards  recommenced  the  same  hope- 
less toil ;  but  no  sooner  was  the  opening  closed,  and  the 
water  retained  in  the  stomach,  from  whence  it^was  absorbed 
into  the  system,  than  thirst  quickly  vanished  ^V 

In  studying  the  history  of  a  language,  it  is  often  most 
important  to  bear  in  mind  that  words  ultimately  derived 
from  one  language  are  proximately  derived  through  the 
medium  of  another.  Thus,  there  will  occur  to  the 
reader  numberless  English  words  which  have  been  de- 
rived from  the  Latin  through  the  French,  as,  for  instance, 
jtidge,  noble,  emperor,  governor,  prince.  And,  to  quote 
M.  Brachet  : — 

'  When  Jerome  translated  the  Old  Testament  into  Latin,  he 
incorporated  into  his  version  certain  Hebrew  words  which 
had  no  Latin  equivalents,  as  seraphim,  Gehenna,  pascha,  &c.: 
from  Latin  they  passed  at  a  later  time  into  French  {st^raphin, 
gene,  pdque).  Rut  they  entered  French  from  the  Latin,  not 
from  the  Hebrew.  The  same  is  the  case  with  the  Arabic ; 
its  relations  with  French  have  been  purely  accidental.  To 
say  nothing  of  those  words  which  express  oriental  things, 
such  as  A/coran,  bey,  cadi,  caravane,  derviche,  firman, 
janissaire,  &c,  which  were  brought  into  the  west  by 
travellers,  the  French  language  received,  in  the  middle  ages, 
many  Arabic  words  from  another  source  :  the  Crusades,  the 


62 


Lewes'  Physiology  of  Common  Life,  vol.  i.  pp.  45-47 


TO  INDUCTION-, 


321 


scientific  greatness  of  the  Arabians,  the  study  of  oriental 
philosophies,  much  followed  in  France  between  the  twelfth 
and  fourteenth  centuries,  enriched  the  vocabulary  of  the  lan- 
guage with  many  words  belonging  to  the  three  sciences 
which  the  Arabians  cultivated  successfully  :  in  astronomy  it 
gave  such  words  as  azimuth,  nadir,  zenith;  in  alchemy, 
alcali,  alcool,  alambic,  alchimie,  elixir,  sirop  j  in  mathe- 
matics, alglbre,  zero,  chiffre.  But  even  so  these  words  did 
not  come  directly  from  Arabic  to  French  ;  they  passed 
through  the  hands  of  the  scientific  Latin  of  the  middle  ages. 
In  fact,  the  oriental  languages  have  had  little  or  no  popular 
or  direct  influence  on  French  *''.' 

The  non-recognition  of  these  intermediate  channels, 
through  which  the  words  of  one  language  have  been 
introduced  into  another,  has  often  led  to  the  most  erro- 
neous theories  as  to  the  connexion  of  languages  or  the 
relations  subsisting  between  the  people  speaking  them. 
Thus,  it  was  once  a  favourite  theory  that  all  languages 
are  derived  from  Hebrew,  and  the  occurrence  in  dif- 
ferent languages  of  the  same  words  has  often,  without 
any  other  ground,  been  regarded  as  a  proof  of  the  con- 
nexion of  the  most  diverse  races. 

I  add  an  example  from  the  science  of  Political 
Economy.  It  has  often  been  supposed  that  high  prices 
produce  high  wages.  A  sudden  rise  in  the  price  of  any 
particular  class  of  commodities  may  lead,  by  a  desire 
on  the  part  of  the  producers  to  increase  the  supply,  and 
by  a  consequent  increase  in  the  demand  for  labour  in 
that  particular  department,  to  a  temporary  rise  in  wages. 

•"  Historical  Grammar,  Translation,  p.  22,  note  2  ;  7th  ed.  p.  27, 
note  2. 


322 


FALLACIES  INCIDENT 


But  a  rise  in  prices  produces  no  permanent  rise  in  wages, 
unless  it  leads  to  an  increased  accumulation  of  capital, 
that  is,  an  augmentation  of  the  fund  available  for  the 
further  production  of  wealth  and,  consequently,  for  the 
payment  of  wages  «^      Here  the  rise  in  prices   is   the 
remote  or  primary,  and  the  increased  accumulation  of 
capital  is  the  proximate,  cause  of  the  phenomenon ;  but, 
as  counteracting  causes,  such  as  reckless  speculation  or 
the  adoption  of  a  more  luxurious  style  of  living  on  the 
part  of  the  capitalists,  may  prevent  the  rise  in  prices 
from  being  followed   by  an  increased  accumulation  of 
capital,  it  is  often  of  great  importance  to  distinguish  the 
two. 

I  have,  thus  far,  discussed  those  errors  which  originate 
in  overlooking  the  presence  of  some  third  circumstance. 
But,  even  when  all  the  circumstances  except  the  cause 
and. effect  (or  what  we  suppose  to  be  such)  have  been 
eliminated,  we  may  still  commit  an  error,  either  from 
mistaking  the  cause  for  the  effect,  or  from  neglecting  to 
take  account  of  their  mutual  action  and  reaction  and 
being  thus  led  erroneously  to  assign  to  one  of  the  two 
exclusively  the  whole  share   in   the   production  of  the 

ultimate  effect. 

(5)  The  importance  of  not  overlooking  this  latter 
source  of  error  is  well  illustrated  by  the  following  remarks 
of  Sir  G.  C.  Lewis «'  :— 

•*  See  Mill's  Political  Economy,  I^k.  II.  ch.  xi.  §  2. 

*5  On  Methods  of  Observation  and  Reasoning  in  Politics,  vol.  1. 

p.  375- 


TO  INDUCTION 


Z'^?> 


*  An  additional  source  of  error  in  determining  political 
causation  is  likewise  to  be  found  in  the  7nutuality  of  cause 
and  effect.     It  happens  sometimes  that,  when  a  relation  of 
causation  is  established   between   two   facts,  it  is   hard  to 
decide  which,  in  the  given  case,  is  the  cause  and  which  the 
effect,  because  they  act  and  re-act  upon  each  other,  each 
phenomenon  being  in  turn  cause  and  effect.     Thus,  habits 
of  industry  may  produce  wealth  ;    while  the  acquisition  of 
wealth  may  promote  industry' :  again,  habits  of  study  may 
sharpen  the  understanding,  and  the  increased  acuteness  of 
the  understanding  may  afterwards  increase  the  appetite  for 
study.     So  an  excess  of  population  may,  by  impoverishing 
the  labouring  classes,  be  the  cause  of  their  living  in  bad 
dwellings ;  and,  again,  bad  dwellings,  by  deteriorating  the 
moral  habits  of  the  poor,  may  stimulate  population.     The 
general  intelligence  and  good  sense  of  the  people  may  pro- 
mote its  good  government,  and  the  goodness  of  the  govern- 
ment may,  in  its  turn,  increase  the  intelligence  of  the  people, 
and  contribute  to  the  formation  of  sound  opinions  among 
them.     Drunkenness  is  in  general  the  consequence  of  a  low 
degree   of  intelligence,  as   may  be   observed  both   among 
savages  and  in  civilized  countries.     But,  in  return,  a  habit  of 
drunkenness  prevents  the   cultivation  of  the   intellect,  and 
strengthens  the   cause   out   of  which   it  grows.      As  Plato 
remarks,  education  improves  nature,  and  nature  facilitates 
education.     National   character,   again,   is   both   effect   and 
cause  :  it  re-acts  on  the  circumstances  from  which  it  arises. 
The  national  peculiarities   of  a   people,   its  race,   physical 
structure,  climate,   territory,  «S:c.,  form  originally  a  certain 
character,  which  tends  to  create  certain  institutions,  political 
and  domestic,  in  harmony  with  that  character.     These  insti- 
tutions strengthen,  perpetuate,  and  reproduce  the  character 
out  of  which  they  grew,  and  so  on  in  succession,  each  new 
effect  becoming,  in  its  turn,  a  new  cause.     Thus  a  brave, 
energetic,  restless  nation,  exposed  to  attack  from  neighbours, 

Y   2 


3^4 


FALLACIES  INCIDENT 


organises  military  institutions:  these  institutions  promote 
and  maintain  a  warlike  spirit :  this  warlike  spirit,  again 
assists  the  development  of  the  military  organisation,  and 
it  is  further  promoted  by  territorial  conquests  and  success  in 
war,  which  may  be  its  result-each  successive  effect  thus 
adding  to  the  cause  out  of  which  it  sprung. 

The  difference  between  the  calculated  and  observed 
velocities  of  sound  (already  noticed'''')  furnishes  another 
illustration  of  the  importance  of  attending  to  the  mutual 
action  of  cause  and  effect.     The  wave  of  sound,  in  its 
passage  through  the  air,  developes  heat  by  compression, 
and  this  heat,  by  augmenting  the  elasticity  of  the  air, 
increases,  in    turn,  the  velocity  with  which  the  sound 
is  transmitted.     Thus  the  effect  re-acts  upon,  and  pro- 
motes the  operation  of,  the  original  cause.     It  was  from 
overlooking  this  fact  that  Newton's  calculation  of  the 
velocity  of  sound  fell  short  of  the  observed  velocity  by 
about  one-sixth  of  the  actual  rate. 

Malthus'  speculations  on  the  increase  of  population 
illustrate  another  form  of  the  same  error.      He  found 
that,  in  many  cases,  population   increased   faster   than 
food  increased.     He  inferred  that  this  increase  of  popu- 
lation once   begun  would   continue   under   all   circum- 
stances ;  and  that  therefore  a  time  was  at  hand,  in  many 
countries,  when  the  bulk  of  the  people  would  be  reduced 
almost  to  a  state  of  starvation.      He  did  not  observe 
that,  in  this  case,  the  effect  re-acts  upon  the  cause ;  not, 
however,  in  the  way  of  promoting  but  of  retarding  its 

•«  Pp.  181-2. 


TO  INDUCTION, 


'^'^3 


operation.  The  tendency  of  an  increase  of  population 
is  certainly  to  diminish  the  supply  of  food  ;  but,  in 
attempting  to  forecast  the  ultimate  result  of  this  ten- 
dency, Malthus  did  not  take  sufficient  account  of  the 
fact  that  the  diminution  in  the  supply  of  food  has, 
in  its  turn,  a  tendency  to  arrest  the  increase  of  popu- 
lation. 

Instances  of  the  tendency  of  an  effect  to  re-act  upon 
its  cause,  in  the  way  of  diminishing  its  intensity,  are  very 
frequent  in  human  affairs.  Thus,  when  a  man  discovers 
that  he  is  labouring  under  a  disease,  the  additional 
prudence  which  he  is  induced  to  exercise  will  often 
not  only  arrest  or  retard  the  progress  of  the  disease, 
but  lead  to  the  prolongation  of  his  life  beyond  the  usual 
term.  Again,  when  a  deficiency  of  sanitary  arrange- 
ments has  led  to  an  increased  mortality  or  the  outbreak 
of  a  pestilence,  the  attention  thus  directed  to  the  noxious 
influences  at  work  will  often  result  in  their  removal,  or, 
at  least,  in  some  considerable  alleviation  of  them.  It  is 
plain  that,  in  speculating  on  the  future,  these  are  con- 
siderations which  ought  not  to  be  left  out  of  account. 

(6)  We  may  invert  cause  and  effect,  mistaking  one 
for  the  other.  This  error  is  not  infrequent  in  historical 
speculations,  as,  for  instance,  when  some  great  event, 
such  as  the  religious  reformation  of  the  sixteenth  cen- 
tury, or  the  French  Revolution,  is  assigned  as  the  cause 
of  a  general  change  of  opinion  or  of  certain  mental 
and  social  habits,  whereas,  in  reality,  the  gradual,  and 
often  unobserved,  operation  of  this  change  has  been  the 


326 


FALLACIES  INCIDENT 


cause,  and  not  the  effect,  of  the  historical  event.  In 
a  case  of  this  kind,  however,  the  event  may,  in  turn, 
have  intensified,  and,  perhaps,  given  the  sanction  of 
authority  to,  the  causes  which  produced  it. 

Again,  a  particular  form  of  government,  monarchical, 
aristocratical,  democratical,  or  the  like,  is  often  assigned 
as  the  cause  of  certain  peculiarities  of  social  feelmg  or 
national  character,  whereas  it  would  probably  be  far 
more  correct  to  regard  the  form  of  government  as  due, 
in  the  first  instance,  to  these  peculiarities,  though  it,  in 
turn,  may  have  intensified  the  causes  to  which  it  was 

originally  due. 

In  meteorological  speculations  it  has  been  questioned 
whether  the  electrical  phenomenon  of  lightning  is  the 
cause  or  effect  of  the  sudden  precipitations  of  rain  and 
hail  which  it  generally  accompanies.  Sir  John  Herschel 
(in  opposition  to  the  ordinary  opinion ^^)  maintains  that 
it  is  the  effect,  and  argues  thus  :— 

'  Whatever  may  be  the  state  of  the  ultimate  molecules  of 
vapour,  it  seems  impossible  but  that  when  a  great  multitude 
of  them  lose  their  vaporous  state  by  cold,  and  coalesce  mto 
a  drop  or  snow  spangle,  however  minute,  that  drop  will  have 
collected  and  retained  on  its  surface  (according  to  the  laws 
of  electric  equilibrium)  the  whole  electricity  of  its  constituent 
molecules,  which  will  therefore  have  some  finite,  though  very 
feeble  tension.  Now,  suppose  any  number  ( looo  for  instance) 
of  such  globules  to  coalesce,  or  that  by  successive  deposition 
one  should  gradually  grow  to  icoo  times  its  original  volume. 
The  diameter  will  be  only  lo,  and  the  surface  loo  times 

"  Hersohel's  Meteorolofy,  %%  i35»  '37- 


TO  INDUCTION 


327 


increased.  But  the  electric  contents,  being  the  sum  of  those 
of  the  elementary  globules,  will  be  increased  one  thousand- 
fold, and,  being  spread  entirely  over  the  surface,  will  have  a 
tenfold  density  (z.  e.  tension). 

♦  »****♦ 

*  It  will  easily  be  seen  that,  when  thousands  of  these 
electriferous  globules  again  further  coalesce  into  rain  drops, 
a  great  and  sudden  increase  of  tension  at  their  surface  must 
take  place.  Their  electricity,  then,  is  enabled  to  spring  from 
drop  to  drop,  and,  rushing  in  an  instant  of  time  from  all  parts 
of  the  cloud  to  the  surface,  a  flash  is  produced.  Accordingly, 
in  thunder-storms,  it  is  the  commonest  of  all  phenomena  to 
find  each  great  flash  succeeded  by  a  sudden  rush  of  rain  at 
such  an  interval  of  time  as  may  be  supposed  to  have  been 
occupied  in  its  descent.  The  sudden  precipitation  of  large 
quantities  of  rain,  and  especially  of  hail,  which  is  formed  in 
a  cold  region,  where  the  insulating  power  of  the  air  is  great, 
is  almost  sure  to  be  accompanied  with  lightning,  which  the 
usual  perversity  of  meteorologists,  where  electricity  is  in 
question,  long  persisted,  and  even  yet  persists,  with  few  ex- 
ceptions, in  regarding  as  the  cause,  and  not  the  consequence, 
of  the  precipitation.' 

A  question  has  also  been  raised  whether  the  copious 
precipitation  of  rain  which  usually  takes  place  in  the 
centre  of  a  cyclone  is  the  cause  or  the  effect  of  the 
cyclone.  The  more  probable  view  is  that  the  partial 
vacuum  produced  by  the  rain-fall,  and  the  consequent 
inrush  of  the  surrounding  atmosphere,  is  the  cause  of 
the  cyclone. 

Mr.  M'Lennan,  in  his  Primitive  Marriage,  conceives 
that  marriage  by  capture  arose  from  the  custom  of 
exogamy,  that  is  to  say,  from  the  custom  which  forbad 


328 


FALLACIES  INCIDENT 


marriage  within  the  tribe.  Sir  John  Lubbock-,  on  the 
other  hand,  opposes  this  opinion,  and  regards  exogamy 
as  arising  from  marriage  by  capture,  not  marriage  by 
capture  from  exogamy.  'Mr.  M'Lennan's  theory,'  says 
he  *  seems  to  me  quite  inconsistent  with  the  existence 
of'tribes  which  have  marriage  by  capture  and  yet  are 
endogamous.  The  Bedouins,  for  instance,  have  un- 
mistakeably  marriage  by  capture,  and  yet  the  man  has 
a  right  to  marry  his  cousin,  if  only  he  be  willing  to  give 
the  price  demanded  for  her.'  ^ 

Professor  Rogers,  in  his  Manual  of  Political  Economy  , 
calls  in  question  the  received  opinion  on  the  relation 
between  the  increase  of  population  and  the  cultivation 
of  inferior  soils.  Though  I  cannot  accept  his  position, 
the  passage  will  serve  as  an  instance  of  the  difficulty 
frequently  experienced  in  determining  which  of  two 
phenonicna  or  events  is  cause  and  which  is  effect. 

'  There  is  not  a  shadow  of  evidence  in  support  of  the  state- 
ment that  inferior  lands  have  been  occupied  and  cultivated 
as  population  increases.  The  increase  of  population  has  not 
nreceded  but  followed  this  occupation  and  cultivation.  It  is 
not  the  pressure  of  population  on  the  means  of  subsistence 
which  has  led  men  to  cultivate  inferior  soils,  but  the  fact  that 
these  soils  being  cultivated  in  another  way,  or  taken  into 
cultivation,  an  increased  population  became  possible.  How 
could  an  increased  population  have  stimulated  greater  labour 
in  agriculture,  when  agriculture  must  have  supplied  the 
means  on  which  that  increased  population  could  have  ex- 

•«  Origin  of  Civilization  and  Primitive  Condition  of  Man,  ch.  3. 
••  p.  153. 


TO  INDUCTION. 


329 


isted  ^"  ?  To  make  increased  population  the  cause  of  im- 
proved agriculture  is  to  commit  the  absurd  blunder  of 
confounding  cause  and  effect.' 

While  agreeing  with  the  ordinary  theory  that  the 
pressure  of  population  leads,  in  the  first  instance,  to 
the  cultivation  of  inferior  lands,  I  should  admit  that  the 
greater  area  of  land  under  cultivation,  by  rendering 
possible  a  larger  population,  reacts  upon  and  intensifies 
the  original  cause,  an  increased  population  leading  to  the 
cultivation  of  fresh  lands,  that  rendering  possible  a  still 
larger  population,  this  in  turn  leading  to  the  cultivation 
of  fresh  lands,  and  so  on,  till  the  process  is  arrested 
by  counteracting  causes.  If  this  view  be  correct,  the 
ordinary  theory  is  more  justly  open  to  the  charge  of 
neglecting  to  take  into  account  the  '  mutuahty '  of  cause 
and  effect,  noticed  a  few  pages  back,  than  of  inverting 
their  relation. 

VI.  The  Argument  from  Analogy,  as  has  already  been 
stated,  consists  in  drawing  the  conclusion  that,  because 
two  or  more  phenomena  resemble  each  other  in  certain 
observed  points,  they  also  resemble  each  other  in  certain 
other  points  beyond  the  range  of  our  observation.  The 
conditions  with  which  such  an  inference,  in  order  to  be 
legitimate,  must  conform,  need  not  be  here  repeated.  If 
the  conditions  be  not  fulfilled,  we  may  commit  the  error 


70 


This  question  appears  to  ignore  the  fact  that  a  population  mav 
have  an  insufficient  supply  of  food,  though  what  it  does  possess  ma) 
be  just  competent  to  sustain  life. 


330 


FALLACIES  INCIDENT 


either  of  over-estimating  the  force  of  the  analogy ;  of 
mistaking  the  direction  in  which  it  points,  so  as  to  regard 
an  analogy  which  makes  against  a  certain  position  as 
making  for  it,  or  the  reverse  ;  or,  lastly,  of  supposing 
grounds  of  analogy  to  subsist  where  there  are  really 
none.  The  two  former  errors  have  been  sufficiently  ex- 
emplified in  the  chapter  on  Imperfect  Inductions. 

When  we  exaggerate  the  value  of  analogical  evidence, 
or  mistake  the  conclusion  to  be  drawn  from  it,  we  may 
be   led   to  do  so  either   by  over-rating  the  number  of 
ascertained    points   of   resemblance   as   compared   with 
ascertained  points  of  difference,  or  the  reverse,  or  by 
miscalculating  the  extent  of  our  knowledge  of  the  pheno- 
mena.    The  examples  referred  to  illustrate  both  sources 
of  error.     Thus,  for  instance,  the  points  in  which  elec- 
tricity resembles  a  fluid  are  obvious,  while  the  points  of 
difference  are  far  less  obtrusive,  and,  moreover,  the  un- 
known properties  of  electricity  are  probably  out  of  all 
proportion  to  those  which  we  know.     In  this  case,  too, 
when  we  include  the  consideration  of  heat,  light    and 
similar   agencies,   the   argument   from   analog)-  may  be 
used  against,  rather  than  in  favour  of,  the  identification 
of  electricity  with  a  fluid. 

The  student  need,  however,  hardly  be  reminded  that 
an  analogy  which  in  one  state  of  knowledge  appears 
to  be  a  strong  one  may,  as  knowledge  advances,  become 
extremely  faint,  worthless,  or  even  positively  unfavourable 
to  the  position  which  it  was  originally  adduced  to  support. 
The  term  False  Analogy  is,  strictly  speaking,  applied 


TO  INDUCTION, 


Z?^^ 


not  to  those  cases  in  which  we  over-estimate  the  value 
of  the  analogy,  or  mistake  the  direction  in  which  the 
argument  points,  but  to  those  cases  of  analogical  in- 
ference in  which  there  exists  no  ground  for  any  analogy 
whatever.     Two  phenomena.  A,  B,  resemble  each  other 
in  the  possession  of  the  properties  a,  b,  c.     The  pheno- 
menon A  is  observed  also  to  present  the  property  d,  and 
hence  it  is  inferred  as  probable  that  the  same  property 
is  to  be  found  also  in  B.    Now  it  has  already  been  pointed 
out  that  if  we  have  any  special  reason  for  supposing  d  to 
be  causally  connected  with  any  of  the  properties  a,  b,  c, 
the  argument  ceases  to  be  analogical,  and  becomes  in- 
ductive.    But  if,  on  the  other  hand,  we  have  any  special 
reason  for  supposing  that  d  is  causally  connected  with 
none  of  the  properties  a,  b,  c,  there  is  no  room  for  any 
inference  whatever.     The  whole  force  of  the  Argument 
from  Analogy  consists  in  the  chance  of  d  being  causally 
connected  with  a,  b,  or  c\  if  we  have  reason  to  believe 
that  this  is  the  case,  the  argument  becomes  more  than 
analogical ;  if  we  have  reason  to  believe  that  it  is  not 
the  case,  we  are  debarred  from  employing  the  argument 
altogether.     Thus,  in  a  certain  sense,  the  Argument  from 
Analogy  is  based  on  our  ignorance ;  it  is  the  result  of 
a  calculation  of  chances,  which  an  accession  of  know- 
ledge may  invalidate,  by  either  augmenting,  diminishing, 
or  annihilating  it.     Of  False  Analogy,  in  its  strict  sense, 
that  is  to  say,  the  error  of  supposing  that  similarity  or 
dissimilarity  in  certain  points  is  an  evidence  of  similarity 
or  dissimilarity  in  other  points,  when  more  careful  re- 


332 


FALLACIES  INCIDENT 


flexion  or  observation  would  lead  to  the  belief  that  there 
is  probably  no  connexion  whatever  between  the  ob- 
served points  from  which  the  Analogy  proceeds  and  the 
unobserved  points  to  which  it  argues,  instances  are 
extremely  numerous  in  almost  every  branch  of  knowledge. 
As  this  form  of  Fallacy  is  so  common,  I  shall  subjoin 
several  examples  of  it. 

The  following  excellent  illustration  is  quoted  by  Mr. 
Mill  from  Archbishop  Whately's  Rhetoric'^^  \ 

'  It  would  be  admitted  that  a  great  and  permanent  diminu- 
tion in  the  quantity  of  some  useful  commodity,  such  as  com, 
or  coal,  or  iron,  throughout  the  world,  would  be  a  serious  and 
lasting  loss;  and  again  that,  if  the  fields  and  coal  mines 
yielded  regularly  double  quantities  with  the  same  labour,  we 
should  be  so  much  the  richer  :  hence  it  might  be  inferred 
that,  if  the  quantity  of  gold  and  silver  in  the  world  were 
diminished  one  half,  or  were  doubled,  like  results  would 
follow  ;  the  utility  of  these  metals,  for  the  purposes  of  coin, 
being  very  great.  Now  there  are  many  points  of  resem- 
blance and  many  of  difference  between  the  precious  metals 
on  the  one  hand,  and  corn,  coal,  &c.  on  the  other  :  but  the 
important  circumstance  to  the  supposed  argument  is  that  the 
utility  of  gold  and  silver  (as  coin,  which  is  far  the  chief) 
depends  on  their  value^  which  is  regulated  by  their  scarcity, 
or  rather,  to  speak  strictly,  by  the  difificulty  of  obtaining 
them  ;  whereas,  if  corn  and  coal  were  ten  times  as  abundant 
(i.e.  more  easily  obtained),  a  bushel  of  either  would  still  be 
as  useful  as  now.  15ut  if  it  were  twice  as  easy  to  procure 
gold  as  it  is,  a  sovereign  would  be  twice  as  large  ;  if  only 

'^  Mill's  Logic,  Bk.  V.  ch.  v.  §  6 ;  Whately's  Rhetoric,  Part  I. 
ch.  ii.  §  7.  The  passage  does  not  occur  in  the  earlier  editions  of 
Whately's  Rhetoric. 


TO  INDUCTION, 


yhz 


half  as  easy,  it  would  be  of  the  size  of  a  half-sovereign,  and 
this  (besides  the  trifling  circumstance  of  the  cheapness  or 
dearness  of  gold  ornaments)  would  be  all  the  difference. 
The  analogy,  therefore,  fails  in  the  point  essential  to  the 
argument.' 


Respect  for  antiquity  is  often  urged  by  an  argument 
so  sweeping  as  to  assume  the  form  of  a  False  Analogy. 
*  Who  are  we,'  it  is  said,  *  that  we  should  presume  to 
think  that  we  know  better  than  previous  generations?' 
Now,  on  many  matters  of  fact,  there  can  be  no  question 
that  the  belief  of  previous  generations,  when  properly 
examined  and  sifted,  must  be  accepted  as  final,  inasmuch 
as  they  vere  contemporary,  or  nearly  contemporary, 
with  the  original  sources  of  information.  To  infer  from 
this  just  and  limited  deference  the  necessity  of  an  undis- 
criminating  submission  to  the  opinions  of  our  ancestors, 
would  be  an  instance  of  the  fallacy  of  Inductio  per 
Enumerationem  Simplicem.  But  this,  at  least  in  many 
cases,  seems  not  to  be  the  nature  of  the  argument,  which 
appears  rather  to  proceed  on  some  such  grounds  as 
these :  we  reverence  the  opinions  of  the  aged,  because 
they  have  had  more  experience  than  we  have  had,  and 
therefore,  surely,  on  the  same  principle,  we  ought  to 
accept  the  opinions  of  our  ancestors,  who  lived  in  bygone 
generations.  The  point  of  resemblance  is  the  fact  of 
having  been  born  at  a  period  prior  to  ourselves,  and 
hence  it  is  inferred  that  the  greater  experience  and  the 
greater  wisdom  which  are  found  to  be  concomitants  of 
this  fact  in  the  case  of  many  of  our  senior  contemporaries 


334 


FALLACIES  INCIDENT 


may  also  be  presumed  in  the  case  of  those  who  have 
long  since  been  dead.  It,  of  course,  escapes  the  notice 
of  those  who  have  recourse  to  this  argument,  that  the 
average  age  of  the  persons  living  at  any  one  time  is 
about  the  same  as  that  of  those  living  at  any  other,  and 
that  superior  wisdom  is  the  consequence  not  of  priority 
of  birth  but  of  greater  experience.  Thus  far,  the  fallacy 
may  be  regarded  as  one  of  False  Analogy,  strictly  so 
called.  But  there  is  another  consideration  which  turns 
the  edge  of  the  argument.  Experience  grows  with  time, 
each  generation  not  only  inheriting  the  accumulated 
experience  of  i)revious  generations,  but  adding  to  the 
stock  its  own  acquisitions.     '  Recte  enim,'  says  Bacon  ''^, 

"  Novum  Organum,  Lib.  I.  A  ph.  Ixxxiv.  In  the  first  edition  of 
this  work  1  sujjgested  that  the  reference  might  possibly  be  to 
.4*;schylus,  I'rometheus  Vinctiis,  1.  981  :  dXX*  iKZihaoKn  irdvO*  o 
yqpdcfKOJv  xp^^^s.  Through  the  courtesy  of  the  Rev.  E.  Marshall, 
I  am  now  enabled  to  supply  the  true  reference,  which  is  to  Aulus 
Gellius,  AW/es  Atticce,  Lib.  XIL  cap.  11  :  '  Alius  quidam  veterum 
poetarum,  cujus  nomen  mihi  nunc  memoriae  non  est,  veritatem  tem- 
poris  filiam  esse  dixit.'  It  has  also  been  pointed  out  to  me  that 
'Veritas  temporis  filia'  is  the  legend  on  the  groats  of  Queen  Mary, 
which  were  doubtless  in  use  in  Bacon's  time.  The  following  sen- 
tences occur  in  the  same  Aphorism  of  the  Novum  Organum :  '  De 
antiquitate  autem  opinio,  quam  homines  de  ipsa  fovent,  ncgligcns 
omnino  est,  et  vix  verbo  ipsi  congrua.  Mundi  enim  senium  et 
grandnevitas  pro  antiquitate  vere  habenda  sunt ;  quae  temporibus 
nostris  tribui  debent,  non  juniori  setati  mundi,  qualis  apud  antiques 
fuit.  Ilia  enim  cetas,  respcctu  nostri,  antiqua  et  major;  respectu 
mundi  ipsius,  nova  et  minor  fuit.  Atque  revera  quemadmodum 
raajorem  rerum  humanarum  notitiam,  et  maturius  judicium,  ab 
homine  sene  expectamus,  quam  a  juvene,  propter  experientiam,  el 
rerum,  quas  vidit,  et  audivit,  et  cogitavit,  varietatem  et  copiam ; 


TO  INDUCTION 


^ZS 


'Veritas  temporis  filia  dicitur,  non  auctoritatis.'     'Anti- 
quitas  saecuh  juventus  mundi ''\' 

Bishop  Wilkins'  Discovery  of  a  New  World  contains 


eodem  modo  et  a  nostra  octate  (si  vires  suas  nosset,  et  experiri  et 
intendere  vellet^  majora  multo  quam  a  priscis  temporibus  expectari 
par  est ;  utpote  aetate  mundi  grandiore,  et  infinitis  experimentis  et 
observationibus  aucta  et  cumulata.'  Bentham  in  his  Book  of  Falla- 
cieSy  Part  I.  ch.  ii.,  and  Sydney  Smith  in  his  review  of  that  work 
{^Edinburgh  Review,  No.  Ixxxiv,  reprinted  in  his  Collected  Works), 
have  some  very  apposite  and  amusing  remarks  on  this  subject. 

"  De   Augmentis   Scientiarum,   Lib.    I.      Dr.    Whewell   in   his 
Philosophy  0/  Discovery  (chap.  xiii.  §  4)  appears  to  think  that  this 
celebrated  Aphorism  may   be   traced    to  Giordano  Bruno.     'It    is 
worthy  of  remark  that  a  thought  which  is  often  quoted  from  Francis 
Bacon,  occurs   in  Bruno's  Cena  di  Cenere,  published  in   1584;    I 
mean,  the  notion  that  the  later  times  are  more  aged  than  the  earlier. 
In  the  course  of  the  dialogue,  the  Pedant,  who  is  one  of  the  inter- 
locutors, says,  "  In  antiquity  is  wisdom  ;  "  to  which  the  Philosophical 
Character  replies,  "  If  you  knew  what  you  were  talking  about,  you 
would  see  that  your  principle  leads  to  the  opposite  result  of  that 
which  you  wish  to  infer  ; — I  mean,  that  we  arc  older,  and  have  lived 
longer,  than  our  predecessors."      He  then  proceeds  to  apply  this 
thought,  by  tracing  the    course  of  astronomy   through  the  earlier 
astronomers  up  to  Copernicus.'     See  Wagner's  edition  of  Giordatio 
Bruno's   IVorks,  vol.  i.  p.  132.     In  the  original  the  passage  runs 
thus : — '  Prudenzio.  Sii  come  la  si  vuole,  io  non  voglio  discostarmi 
dal  parer  de  gli  antichi  ;  per  che  dice  il  saggio :  Ne  1'  antiquita  e  la 
sapienza.      Teojilo.    E  soggiunge  :    In  molti  anni  la  prudenza.     So 
voi  intendeste  bene  quel  che  dite,  vedreste,  che  dal  vostro  fondamento 
s'  inferisce  il  contrario  di  quel  che  pensate  :    voglio  dire,  che  noi 
siamo  piu  vecchi  et  abbiamo  piu  lunga  eta,  che  i  nostri  predecessori.' 
Mr.  Spedding,  however,  in  his  edition  of  Bacon,  questions  whether 
Bacon  intended  the  aphorism  as  a  quotation,  and  thinks  it  probable 
that  he  did  not  derive  it  from  any  earlier  writer. — See  Ellis  and 
Spedding's  edition  oi  Bacon ^  vol.  i.  p.  458,  n.  4. 


33<5 


FALLACIES  INCIDENT 


the  following  curious  extract,  translated  from  the  work 
of  Cardinal  Nicolo  de  Cusa  De  docta  Ignorantid'^  : 

'  We  may  conjecture  the  inhabitants  of  the  sun  are  like  to 
the  nature  of  that  planet,  more  clear  and  bright,  more  intel- 
lectual than  those  in  the  moon  where  they  are  nearer  to  the 
nature  of  that  duller  planet,  and  those   of  the   earth  being 
more  gross  and  material  than  either,  so  that  these  intellectual 
natures  in  the  sun  are  more  form  than  matter,  those  in  the 
earth  more  matter  than  form,  and  those  in  the  moon  betwixt 
both.     This  we  may  guess  from  the  fiery  influence  of  the  sun, 
the  watery  and  aerous  influence  of  the  moon,  so  also  the 
material  heaviness  of  the  earth.     In  some  such  manner  like- 
wise is  it  with  the  regions  of  the  other  stars ;  for  we  con- 
jecture that  none  of  them  are  without  inhabitants,  but  that 
there  are  so  many  particular  worlds  and  parts  of  this  one 
universe  as  there  are  stars,  which  are  innumerable,  unless  it 
be  to  Him  who  created  all  things  in  number.' 

The  analogy  in  this  case  is  founded  not,  as  in  the 
previous  instances,  on  points  of  resemblance  but  on 
points  of  dissimilarity.  The  sun,  the  moon,  and  the 
earth  are  formed  of  different  materials,  and,  therefore, 
it  is  argued,  their  inhabitants  differ  in  their  intellectual 
capacities,  the  exaltation  of  intelligence  rising  in  pro- 
portion to  the  *  clearness  and  brightness '  of  the  globe 
which  they  inhabit.  Waiving  the  assumptions  as  to  the 
materials  of  which  the  three  bodies  are  composed  and 
the  habitation  of  them  all  by  intelligent  beings,  it  is 
plain  that  there  is  no  presumption  in  favour  of  the 
theory  that  the  intelligence  of  the  inhabitants  stands  in 

'♦  Wilkins'  Discovery  of  a  Nnu   World  in  the  Moon,  p.  ia8  ; 
Cusanus,  De  doctd  Ignorant  id,  Lib.  II.  ch.  xii. 


TO  INDUCTION 


331 


any  relation  to  the  material  of  the  globe  on  which  they 
live ;  by  parity  of  reasoning,  birds  ought  to  be  far  more 
intelligent  than  men. 

The  following  passage  from  Bacon's  Novum  OrganutJi^^ 
furnishes  a  remarkable  example  of  a  combination  of 
Confusion  of  Language  with  False  Analogy :  '  Sed 
temporibus  insequentibus,  ex  inundatione  Barbarorum 
in  imperium  Romanum,  postquam  doctrina  humana 
velut  naufragium  perpessa  esset ;  tum  demum  philo- 
sophise Aristotelis  et  Platonis,  tanquam  tabulae  ex 
materia  leviore  et  minus  solida,  per  fluctus  tem.porum 
servatai  sunt.'  The  student  may  exercise  his  sagacity 
in  assigning  its  due  share  to  each  source  of  deception. 

The  arguments  for  or  against  the  independence  of 
colonies  will  often  be  found  to  rest  on  a  False  Analogy. 
Sometimes  it  is  said  that,  under  no  circumstances,  ought 
a  colony  to  rebel  against  the  authority  of  the  mother- 
country;  at  other  times,  that,  the  colony  having  come  to 
maturity,  the  time  for  its  emancipation  has  arrived.  In 
each  of  these  cases  the  argument  is  suggested  by  the 
term  *  mother-country.'  Now  the  relations  of  the  child 
to  the  parent  are  mainly  determined  by  natural  affection, 
by  early  associations,  by  gratitude  for  favours  received, 
and  frequently  by  the  fact  that,  while  the  child  is  gra- 
dually approaching  to  the  prime  of  life,  the  parent 
is  gradually  receding  from  it.  Similar  circumstances, 
though  to  a  far  weaker  degree,  may  undoubtedly  de- 
termine the  relations  of  a  colony  to  its  'mother-country,' 

'^  Lib.  I.  Aph.  Ixxvii. 
Z 


33« 


FALLACIES  INCIDENT 


as,  for  instance,  sympathy  of  race,  the  associations  of 
many  of  the  colonists  with  their  early  home,  gratitude 
for  assistance  received  at  the  foundation  of  the  colony 
or  during  the  earlier  years  of  its  existence,  the  growing 
prosperity  of  the  colony  or  the  waning  power  of  the 
*  mother-country.'     But,  in  addition  to  the  fact  that  there 
are  many  cases  in  which  these  circumstances  or  some 
of  them  do   not  exist,  or    in  which  they  exist  only  to 
the  slightest  extent,  it  must  be  plain,  on  reflexion,  that 
the  justice  or  injustice,  the  expediency  or  inexpediency, 
of  separation  from  the  mother-country  or   of  repudia- 
tion by  it  must  often  be  settled  by  considerations  totally 
distinct  from  these,  and  such  as  receive  no  elucidation 
whatever  from  the  relations  between  parent  and  child. 

The  illusion,  originating  in  a  false  analogy,  that  every 
community  must,  like  every  individual  man,  pass  through 
the  three  stages  of  growth,  vigour,  and  decay,  is  thus 
exposed  by  Sir  G.  C.  Lewis  ^« : 

^«  Methods  of  Observation  and  Reasoning  in  Politics,  vol.  ii.  p. 
438.     The  Rev.  E.  H.  Hansell  has  pointed  out  to  me  a  striking 
passage  in  Burke's  '  Letters  on  a  Regicide  Peace,'  in  which  Sir  G.  C. 
Lewis'  notice  of  this  fallacy  is  anticipated  :  *  I  am  not  quite  of  the 
mind  of  those  speculators  who  seem  assured  that  necessarily,  and  by 
the  constitution  of  things,  all  states  have  the  same  periods  of  infancy, 
manhood,  and  decrepitude,  that  are  found  in  the  individuals  who 
compose  them.     Parallels  of  this  sort  rather  furnish  similitudes  to 
illustrate  or  to  adorn,  than  supply  analogies  from  whence  to  reason. 
The  objects  which  are  attempted  to  be  forced  into  an  analogy  are 
not  found  in  the  same  classes  of  existence.     Individuals  are  physical 
beings,  subject  to  laws  universal  and  invariable.     The  immediate 
cause  acting  in  these  laws  may  be  obscure :  the  general  results  are 
subjects  of  certain  calculation.     But  commonwealths  are  not  physical 


TO  INDUCTION 


339 


*  From  what  has  been  already  said,  it  follows  that  the  com- 
parison which  is  sometimes  instituted  between  the  progress 
of  a  community  and  the  life  of  a  man  fails  in  essentials,  and 
is   therefore   misleading.     Both    a   man  and  a  community, 
indeed,  advance  from  small  beginnings  to  a  state  of  maturity  : 
butr  a  man  has  an  allotted  term  of  life,  and  a  culminating 
point  from  which  he  descends ;  whereas  a  community  has  no 
limited  course  to  run  ;  it  has  no  necessary  period  of  decline 
and   decay,    similar  to  the  old  age  of  a  man  ;  its  national 
existence  does  not  necessarily  cease  within  a  certain  time. 
Nations,  as   compared  with  other  nations,  have  periods  of 
prosperity  and  power ;  but  even  these  periods  often  ebb  and 
flow,  and  when  a  civilised  nation  loses  its  pre-eminence — as 
Italy  in  the  nineteenth,  as  compared  with  Italy  in  the  four- 
teenth and  sixteenth  centuries -it  does  not  necessarily  lose 
its  civilisation.    A  political  community  is   renewed  by  the 
perpetual  succession  of  its  members;  new  births,  immigra- 
tions, and  new  adoptions  of  citizens,  keep  the  political  body 
in  a  state  of  continuous  youth.     No  such  process  as  this  takes 
place  in  an  individual  man.     If  he   loses  a  limb,  it  is  not 
replaced  by  a  fresh  growth.     The  effects  of  disease  are  but 
partially  repaired ;  all  the  bodily  and  mental  functions  are 
gradually  enfeebled,  as  life  is  prolonged,  till  at  last  decay  in- 
evitably ends  in  death :  whereas  a  community  might,  con- 
sistently with  the  laws   of  human   nature,  have  a  duration 
co-extensive  with  that  of  mankind. 

*  The  supposed  analogy  between  the  existence  of  a  political 
community  and  the  life  of  a  man  seems  to  have  contributed 
to  the  formation  of  the  belief  in  a  liability  to  corruption^ 
inherent  in  every  society.     It  was  a  favourite  doctrine  among 

but  moral  essences.  They  are  artificial  combinations,  and,  in  their 
proximate  efficient  cause,  the  arbitrary  productions  of  the  human 
mind.  We  are  not  yet  acquainted  with  the  laws  which  necessarily 
influence  the  stability  of  that  kind  of  work  made  by  that  kind  of 
agent.' — VVoiks,  vol.  viii.  pp.  78,  79. 

Z  2 


340 


FALLACIES  INCIDENT 


some  writers  of  the  last  century  that  every  civihsed  com- 
munity  is  fated   to  reach  a  period   of  corruption,  when  its 
healthy  and  natural  action  ceases,  and  it  undergoes  some 
great  deterioration.     The   notion   of  an  inevitable  stage  ot 
corruption  in  a  nation  was,  indeed,  partly  suggested  by  the 
commonplaces  condemnatory  of  luxury,  derived  both   from 
the   classical   and   ecclesiastical  writers;   and  by  the   more 
modern  eulogies  of  savage  life.     So  far,  however,  as  it  was 
founded  on  the   inevitable  periods  of  decay  in  animal  and 
vegetable   life,  the   comparison  was   delusive ;   for   the   two 
relations  which   are   brought   together  do   not  correspond. 
The    death   of   individuals   may,  indeed,  be   considered   a 
necessary  condition  for  the  progress  of  the  society,  into  which 
they  enter  as  temporary  elements.    It  is  by  the  substitution 
of  new  intelligences,   and   of  natures  not   hardened  to  old 
customs,  for  minds  whose  thoughts  and  habits  have  learnt  to 
move  uniformly  in  the  same  groove,  that  progressive  changes 
in  human  affairs  are  effected.  The  decay  and  death  of  the  in- 
dividual, therefore,  tends  not  only  to  prevent  the  deterioration 
of  the  society,  but  to  promote  its  improvement.' 

Ancient  medicine  was  full  of  false  analogies.     I  select 
the  following  examples  from  Dr.  Paris '' : 

*  An  example  of  reasoning  by  false  analogy  is  presented 
to  us  by  Paracelsus,  in  his  work  de  vitd  longA,  wherein, 
speaking  of  antimony,  he  exclaims,  "  Sicut  antimomum  finit 
aurum,  sic,  eadem  ratione  et  forma,  corpus  humanum  purum 
reddit." ' 

The  alchemists,  or  some  of  them,  appear  to  have 
imagined  that  the  same  preparation  by  which  they  hoped 
to  convert  the  baser  metals  into  gold  (called  metaphori- 
cally '  the  healthy  man ')  would  also  be  effective  in  re- 

'■^  Pharmacologia,  p.  64. 


TO  INDUCTION, 


341 


moving  the  sources  of  all  bodily  diseases.  Why  should 
not  the  impurities  of  the  human  body  be  removable  by 
the  same  means  as  the  impurities  of  the  metals  ? 

'They  [that  is,  the  Arabian  physicians]  conceived  that  gold 
was  the  metallic  element  in  a  state  of  perfect  purity,  and  that 
all  the  other  metals  differed  from  it  in  proportion  only  to  the 
extent  of  their  individual  contamination ;  and  hence  the  origin 
of  the  epithet  base^  as  applied  to  such  metals.  This  hypo- 
thesis explains  the  origin  of  alchemy ;  but  in  every  history 
we  are  informed  that  the  earlier  alchemists  expected,  by  the 
same  means  that  they  hoped  to  convert  the  baser  metals  into 
gold,  to  produce  an  universal  remedy,  calculated  to  prolong 
indefinitely  the  span  of  human  existence. 

*  It  is  difficult  to  imagine  what  connexion  could  exist  in 
their  ideas  between  the  ^^Philosopher's  Stone^'  which  was  to 
transmute  metals,  and  a  remedy  which  could  arrest  the  pro- 
gress of  bodily  infirmity  :  upon  searching,  however,  into  the 
writings  of  these  times,  it  appears  probable  that  this  conceit 
may  have  originated  with  the  alchemists  from  the  applica- 
tion of  false  analogies,  and  that  the  error  was  subsequently 
diffused  and  exaggerated  by  a  misconstruction  of  alchemical 
metaphors.' 

The  old  maxim  that  '  Nature  abhors  a  vacuum,'  the 
curious  belief,  still  prevalent  even  amongst  persons  of 
intelligence,  that  the  weather  changes  with  the  *  changes ' 
of  the  moon,  the  once  fashionable  doctrine  of  the  '  Social 
Contract '  or  '  Original  Compact,*  the  explanation  of 
moral  and  physical  facts  by  applying  to  them  the  con- 
ceptions of  'perfect  numbers'  and  '  regular  solids '^'  the 

™  On  this  subject  the  reader  will  find  some  very  curious  informa- 
tion in  Mill's  Logic y  Bk.  V,  ch.  v.  §  6,  and  Whewell's  History  of  the 
Inductive  Sciences,  Bk.  IV.  ch.  iii.  §  2. 


342 


FALLACIES  IXC  WE  NT 


Pythagorean  theory  of  the  Harmony  of  the  Spheres, 
the  Aristotelian  doctrine  of  the  Mean,  and  innumerable 
other  instances  with  which  the  student  will  meet  m  h.s 
reading,  will  abundantly  illustrate  the  nature  of  False 
Analogy  and  its  frequency  in  the  reasoning  of  early 
Speculators. 

"^K    in    that    un- 


The   Argument    from    Final    Causes 


7«  'Turn  veio  ad  ulteriora  tendens  [intellectus  humanus],  ad 
proximiora  recidit,  videlicet  ad  causas  finales,  qvu.  sunt  plane  ex 
natura  hominis,  potius  quam  universi  :  atque  ex  ^oc  ^o^e  ph.lo- 
sophiam  miris  modis  corrui^eruntZ-Bacon,  Nov.  Org.  Lib.  I.  Aph. 

''to  prevent  misconception,  I  may  at  once  state  that  there  is  an 
employment  of  the  Argument  from  Final  Causes  which  I  behev    to 
be  not  only  perfectly  legitimate,  but  the  highest  expression  of  scien- 
tific truth      The  process  of  Natural  Selection  (for  an  explanation  of 
wh  eh      must  reL  my  readers  to  the  works  of  Darwin,  XV  allace 
and  Herbert  Spencer),   by  eliminating    unfit  types   and   imperfe  t 
organisms  in  the  struggle  for  existence,  has  a  constant  tendency  in 
recourse  of  evolution,  to  produce  exactly  those  results  whidi  best 
correspond  with  the  conditions  of  existence  (a  proposition    I  may 
Xu  in  passing,  which,  in  some  measui.,  may  ^e  exten  ed^^^^^^ 
the  biological  to  the  moral  and  mental  spheres).     Hence  there  is  a 
sense  in  :hich  it  is  true  that  '  Nature  always  acts  for  the  best,  ^d 
that  'Nature  does  nothing  in  vain,'  but  we  are  not  therefore,  juti- 
fied  in  ascribing  to  Nature  the  attributes  of  rationality,  in  crediting 
it  with  conscious  design,  or  in  assimilating  its  processes  to  those  of 
rnan      If,  however,  we  believe  in  an  intelligent  Supreme  Cause  rom 
whom  all  Nature  and  Nature's  laws  have  proceeded,  and  by  whom 
they  are   still  sustained,  it  seems   inevitable  to   suppose  that  the 
results  of  the  Universe,  in  their  totality,  are  effecting  the  designs  of 
this  all-powerful  Being,  numerous  and  inexplicable  as  may  be    he 
apparent  exceptions,  when  regarded  in  isolation.      Moreover,  the 


TO  INDUCTION, 


343 


scientific  form  of  it,  once,  and  even  now  in  some 
circles,  so  widely  prevalent,  which  assumes  that  every 
natural  organism  was  specially  designed  to  subserve 
some  special  object,  and  fashioned,  once  for  all,  in 
immediate  reference  to  that  object,  appears  ultimately 
to  repose  on  a  False  Analogy.  God  or  Nature  (for 
both  terms  are  used)  is  assimilated  to  a  human  arti- 
ficer, and  the  argument  appears  to  rest  on  the  assump- 
tion that  the  motives,  conceptions,  and  contrivances  of 
the  one  may  be  regarded  as  similar  to  those  of  the  other. 
'  Nature  does  nothing  in  vain.'  '  Nature  always  acts  for 
the  best.'  '  Everything  is  designed  for  some  good  pur- 
pose.' These  and  similar  maxims  express  the  general 
principle  on  which  the  argument  rests.  Of  its  applica- 
tion to  special  cases  we  may  take  the  following  examples. 
The  instances  given  by  Bacon,  in  the  Advancement 
of  Learning  and   the  Be  Augmentis''',  when  protesting 

marvellous  results  which  not  only  the  material  but  the  spiritual 
world  reveals  to  us,  especially  when  viewed  in  comparison  with  the 
humble  and  simple  beginnings  to  which  many  now  believe  that  they 
can  be  carried  back,  can  hardly  fail  to  serve  as  an  indication  of  the 
existence  of  that  Supreme  Cause  and  to  suggest  the  attributes  of 
supreme  wisdom,  power,  and  goodness  with  which  it  has  been  the 
habit  or  instinct  of  the  more  cultured  races  of  mankind  to  invest 
Him.  Theories  of  evolution  may  be  so  stated  as  not  to  impair,  but 
indefinitely  to  exalt,  our  ideas  of  the  power,  wisdom,  and  benevo- 
lence of  the  Being  in  whom  Nature  had  its  source. 

^  Advancement  of  Learning,  Bk.  U.  i  Ellis  and  Spedding  sedition, 
vol.  iii.  p.  358\  Cp.  De  Augmentis,  iii.  4.  It  should  be  noticed, 
however,  that  Bacon  allows  the  use  of  Final  Causes  in  what  he  calls 
'  Metaphysic'  Of  the  foregoing  instances,  *  and  the  like,'  he  says 
that  they  are  '  well  enquired  and  collected  in  Metaphysic ;  but  in 


i 
i 


344  FALLACIES  INCIDENT 

against  the  employment  of  Final  Causes  in  physical  en- 
quiries, are  the  following  :  ^  The  hairs  of  the  eyelids  are 
L  a  quickset  and  fence  about  the  sight;  the  firmness 
of  the  skins  and  hides  of  living  creatures  is  to  defend 
them  from  the  extremities  of  heat  or  cold  ;  the  bones 
are  for  the  columns  or  beams,  whereupon  the  frames 
of  the  bodies  of  hving  creatures  are  built ;  the  leaves  of 
trees  are  for  protecting  of  the  fruit ;  the  clouds  are  for 

Physic  they  are  impertinent.'     And  again  :  '  Not  because  these  final 
^Z  ar    not  true,  and  worthy  to  be  enquired,  being  kep^^  wi  h.n 
hTown  province;  but  because  their  excursions  into  the  hm.ts  o 
ph  sical  causes  hath  bred  a  vastness  and  solitude  in  that  track 
What  Bacon  appears  to  mean  (and  the  distinction  is  i.nportant)  is 
Tt  in  extra-physical  speculations,  as  are  those  of  Natura  Theology 
i  'the  study  of 'Metaphysics,'  in  the  ordinary  sense  of  the  term, 
l:  epud    ted),  we  may  argue  from  an  ascertained  case  of  adapta  ion 
to  the  wisdom  or  goodness  of  the  Creator,  but  that  we  are  not  ju  t  - 
fied  in  assuming  adaptation  or  design  as  a  datum  m  physical  mvesti- 
ga  in      Those'  who'  defend  this  use  of  the  argument,  would  reply 
fh.    many  discoveries  (such  as,  notably.  Harvey's  discovery  of  the 
dilation  of  the  blood,  which  set  out  from  observing  the  action  of 
"valves  in  the  veins  of  many  parts  of  the  body,  and  enquiring 
1  their  purpose)  have  been  suggested  by  the  idea  of  adaptation 
wLh   it  maT  be  noticed,  does  not  necessarily  include  the  idea  of 
^CZ^      See  Sir  H.  Acland's  Ilar^dan   Oration    for   1865    and 
Sid  Stewart's  Pkilosopky  of  tke  Human  Mind.  Part  II.  ch  xu 
(Sir  W.  Hamilton's   edition  of  Stewart's  Works,  vol    lu    p.  335, 
&    )       This  fact  may  be,  and,  indeed,  must    be,  admitted   with 
fespect   to   physiological    enquiries  (however  the  adaptation  may 
accounted  L),  and  hence  Bacon's  prohibition  is  certainly  too 

'Itave  discussed  the  subject  of  Final  Causes,  with  special  reference 
to  the  views  of  Bacon,  in  the  Introduction  to  my  edition  of  the 
Novum  Organumj  §  10. 


TO  INDUCTION, 


345 


watering  of  the  earth ;  the  solidness  of  the  earth  is  for 
the  station  and  mansion  of  living  creatures.' 

The  absurd  extent  to  which  the  argument  may  be 
carried  by  speculators  who  attempt  to  find  a  Final 
Cause  for  every  phenomenon  which  falls  under  their 
cognisance,  will  be  plain  from  the  examples  which 
follow.  It  would,  however,  be  unjust  to  charge  these 
absurdities  to  the  account  of  those  writers  of  the  past 
generation  who  took  a  more  sober,  though,  perhaps,  an 
erroneous  view  of  the  argument. 

In  the  TimcBus  of  Plato  ^\  the  construction  of  the 
whole  universe,  and  specially  of  man,  is  explained  on 
the  principle  of  Final  Causes.  The  following  extract 
from  Mr.  Grote's  Plato  ^-  will  serve  as  a  specimen  of  the 
method  there  employed  : 

*  The  Demiurgus,  having  constructed  the  entire  Kosmos, 
together  with  the  generated  Gods,  as  well  as  Necessity  would 
permit— imposed  upon  these  Gods  the  task  of  constructing 
Man  :  the  second-best  of  the  four  varieties  of  animals  whom 
he  considered  it  necessary  to  include  in  the  Kosmos.  He 
furnished  to  them  as  a  basis  an  immortal  rational  soul  (di- 
luted remnant  from  the  soul  of  the  Kosmos)  ;  with  which 
they  were  directed  to  combine  two  mortal  souls  and  a  body. 
They  executed  their  task  as  well  as  the  conditions  of  the  pro- 
blem admitted.  They  were  obliged  to  include  in  the  mortal 
souls  pleasure  and  pain,  audacity  and  fear,  anger,  hope,  appe- 
tite, sensation,  «S:c.,  with  all  the  concomitant  mischiefs.  By 
such   uncongenial  adjuncts  the  immortal  rational  soul  was 

•1  Of  Plato,  Bacon  says  truly,  that  he  '  ever  anchoreth  on  that 
shore.' 

sa  Vol.  iii.  pp.  272-275. 


34<5 


FALLACIES  INCIDENT 


unavoidably  defiled.  The  constructing  Gods,  ho^ff '  t°°^ 
care  ^o  defil  it  as  little  as  possible.  They  reserved  the  head 
as  a  separate  abode  for  the  immortal  soul:  plantmg  the 
mortasoul  apart  from  it  in  the  trunk,  and  estabhshmg  the 

Tctls  an  isthmus  of  separation  ^-''^^^ ^^^^^^^Z 
th^  mortal  soul  was  itself  not  single  but  double  .  inciuam^ 
wo  rjls,  a  better  and  a  worse.     The  Gods  Uept  the  tw^^ 
Darts  separate  ;    placing   the  better  portion  in    he  thoracic 
S  nearer  t^  the  head,  and  the  worse  PO-on  low^^^^^^^^^^ 
in  the  abdominal  cavity  :  the  two  being  divided  from  each 
other  by  the  diaphragm,  built  across  the  body  as  a  wall  of 
parUtion  :  just  as^  in  a  dwelling-house,  the  apartments  c.f  th 
women  are  separated  from  those  of  the  men      Above  the 
diaphracrm,  and  near  to  the  neck,  was  planted  the  energetic, 
Sale:us  contentious  soul;  so  placed  as  to  receive  orders 
easS  from  the  head,  and  to  aid  the  rational  soul  m  keeping 
under  constraint  the  mutinous  soul  of  appetite  .^ich  was 
planted  below  the  diaphragm.     The  immortal  soul  was  fas- 
Sned  or  anchored  in  the  brain,  the  two  mortal  souls  in  the 
no  of  the  spinal  marrow  continuous  with  the  brain  :  which 
line  thus  formed  the  thread  of  connexion  between  the  thre- 
The  heart  was  established  as  an  outer  fortress  for  the  exer 
dse  of  influence  by  the  immortal  soul  over  the  other  two. 
It  !vas  at  the  same  time  made  the  initial  point  of  the  veins 
!1  h^  f    inl^^^  whence  the  current  of  blood  proceeded 

to  pass  forcibly  through  the  veins  round  to  a  1  part  of  the 
boclv  The  purpose  of  this  arrangement  is  that,  when  the 
JaTonal  sou/ denounces  some  proceeding  as  wrong  (either 
on  the  part  of  others  without,  or  in  the  appetitive  soul 
"thin  i^  may  stimulate  an  ebullition  of  anger  in  the  hear  , 
Ind  rn^y  transmit  from  thence  its  exhortations  and  threats 
"rtuTthe  many  small  blood  channels  to  all  the  sensitive 
parts^f  the  body  ;  which  may  thus  be  rendered  obedient 
everywhere  to  the  orders  of  our  better  nature. 

<  m  such  ebullitions  of  anger,  as  well  as  in  moments  of 


TO  INDUCTIOISf. 


347 


imminent  danger,  the  heart  leaps  violently,  becoming  over- 
heated and  distended  by  excess  of  fire.  The  Gods  foresaw 
this,  and  provided  a  safeguard  against  it  by  placing  the  lungs 
close  at  hand  with  the  windpipe  and  trachea.  The  lungs 
were  constructed  soft  and  full  of  internal  pores  and  cavities 
like  a  sponge  ;  without  any  blood,— but  receiving,  instead 
of  blood,  both  the  air  inspired  through  the  trachea,  and  the 
water  swallowed  to  quench  thirst.  Being  thus  always  cool, 
and  soft  like  a  cushion,  the  lungs  received  and  deadened  the 
violent  beating  and  leaping  of  the  heart ;  at  the  same  time 
that  they  cooled  down  its  excessive  heat,  and  rendered  it 
a  more  equable  minister  for  the  orders  of  reason. 

*  The  third  or  lowest  soul,  of  appetite  and  nutrition,  was 
placed  between  the  diaphragm  and  the  navel.  This  region 
of  the  body  was  set  apart  like  a  manger  for  containing  neces- 
sary food;  and  the  appetitive  soul  was  tied  up  to  it  like  a  wild 
beast ;  indispensable  indeed  for  the  continuance  of  the  race, 
yet  a  troublesome  adjunct,  and  therefore  placed  afar  off,  in 
order  that  its  bellowings  might  disturb  as  little  as  possible 
the  deliberations  of  the  rational  soul  in  the  cranium  for 
the  good  of  the  whole.  The  Gods  knew  that  this  appe- 
titive soul  would  never  listen  to  reason,  and  that  it  must 
be  kept  under  subjection  altogether  by  the  influence  of 
phantoms  and  imagery.  They  provided  an  agency  for  this 
purpose  in  the  liver,  which  they  placed  close  upon  the  abode 
of  the  appetitive  soul.  They  made  the  liver  compact,  smooth, 
and  brilliant,  like  a  mirror  reflecting  images  :— moreover, 
both  sweet  and  bitter  on  occasions.  The  thoughts  of  the 
rational  soul  were  thus  brought  within  view  of  the  appetitive 
soul,  in  the  form  of  phantoms  or  images  exhibited  on  the 
mirror  of  the  liver.  When  the  rational  soul  is  displeased, 
not  only  images  corresponding  to  this  feeling  are  impressed, 
but  the  bitter  properties  of  the  liver  are  all  called  forth.  It 
becomes  crumbled,  discoloured,  dark,  and  rough  ;  the  gall 
bladder  is  compressed;    the  veins  carrying  the  blood  are 


348 


FALLACIES  INCIDENT 


blocked  up,  and  pain  as  well  as  -kness  arise     On  the  a,n- 
tr,rv  when  the  rational  soul  is  satisfied,  so  as  to  send  torxn 
Sand  complacent  inspirations,-all  this  bitterness  of  the 
Uvlr  U  tranquUlised,  and  all  its  native  sweetness  called  forth 
The  whole  structure  becomes  straight  and  smooth  ;   and  the 
images  impressed  upon  it  are  rendered  propitious.      It  is 
hufthro'gh  the  liver,  and  by  means  of  these  -ages,  that 
the  rational  soul  maintains  its  ascendancy  over  the  appeti- 
l?ve  soulTeither  to  terrify  and  subdue,  or  to  comfort  and 

'"<  Morfo've;,  the  liver  was  made  to  serve  another  purpose^ 
It  wt  sict  d  as  the  seat  of  the  prophetic  agency ;  which 
he  Gods  considered  to  be  indispensable,  as  a  refuge  and  aid 
for  the  irrational  department  of  man.     Though  this  portion 
iTthe  soul  had  no  concern  with  sense  or  reason,  they  wouM 
nnt  shut  it  out  altogether  from  some  glimpse  of  truth.     1  he 
"e  e  Sns  of  prophecy  were  accordingly  signified  on  the 
ifver    for  the  instruction  and  within  the  easy  view  of  the 
aooe'titTve  soul ;  and  chiefly  at  periods  when  the  functions  of 
X  ra  Lnal  s;ul  are  suspended-either  during  sleep,  o 
disease,  or  fits  of  temporary  extasy.    For  no  man  in  his 
Serfet  senses  comes  under  the  influence  of  a  genuine  pro- 
phetic inspiration.    Sense  and  intelligence  are  often  required 
to  Inte  p  et  prophecies,  and  to  determine  what  is  meant  by 
dr  ams'or  signs'or  prognostics  of  other  ^ind^- ^"^^    -- 
Htion-i  are  received  by  men  destitute  of  sense.    To  receive 
hm  is  he  business  of  one  class  of  men  :  to  interpret  them, 
fr  of  another.     It  is  a  grave  mistake,  though  often  com- 
muted   to  confound  the  two.     It  was  in  order   to Jurn  sh 

pr  "phecy  to  man,  therefore,  that  the  Gods  devised  both  the 
prophecy  t  ,  ^  ,,f^^  jhg  pro. 

structure  and  the  piate  ui  i  ic 

phetic  indications  are  cleariy  marked  upon  it_    but  after 

death  they  become  obscure  and  hard  to  decypher 

'The  spleen  was  placed  near  the  liver,  corresponding  to  it 
on  Ihe  lift  side,  in'order  to  take  off  from  it  any  impure 


TO  INDUCTION. 


349 


or  excessive  accretions  or  accumulations,  and  thus  to  pre- 
serve it  clean  and  pure.* 

Aristotle  constantly  employs  this  method  of  reasoning. 
Thus,  in  a  familiar  passage  of  the  Ethics  «^  he  says  that 
*  if  it  is  better  for  men  to  attain  happiness  through  their 
own  exertions  than  through  chance,  it  is  reasonable  to 
suppose  that  this  will  be  the  case,  since  everything  that 
depends  on  Nature  "  is  in  the  best  possible  condition.' 

From  his  physiological  works  (in  which  the  argument 
is  most  commonly  employed)  it  will  be  sufficient  to  ad- 
duce one  or  two  examples,  which  will  serve  also  to  show 
how  a  preconceived, opinion  may  lead  an  author  to  invent 
false  facts  for  the  purpose  of  supporting  his  theory. 

Having  fixed  the  seat  of  sensation  in  the  heart,  in- 
asmuch as  it  is  in  the  centre  of  the  body,  rather  than 
in  the  brain,  as  some  philosophers  had  done,  it  was 
necessary  to  discover  a  special  function  for  the  brain. 
The  necessity  of  discovering  some  function  for  it  led 
to  the  fiction  of  its  *  coldness,'  which  was  supposed  to 
counteract   the   heat  of  the  heart,  and  so  to  preserve 

"  Eth.  Nic  i.  9  (5).     Et  5*  \ar\v  ovroi  fitKriov  ^  5m  rvxv^  «^5at 
Hovuv,  ((,Koyov  Ix^iv  oi/rcus,  dnip  rd  Acard  <pvffiv,  ws  ol6v  n  KaWiara 

8»  The  student  will  notice  the  transition  from  the  Demiurgus  and 
inferior  gods  of  Plato  to  the  *  Nature  '  of  Aristotle.  '  And  in  this,' 
says  Bacon,  *  Aristotle  is  more  to  be  blamed  than  Plato,  seeing  that 
he  left  out  the  fountain  of  fmal  causes,  namely  God,  and  substituted 
Nature  for  God  ;  and  took  in  fmal  causes  themselves  rather  as  the 
lover  of  logic  than  of  theology.'- 77/^  Dignity  and  Advancement  of 
Learning  (Translation  of  the  De  Augrnentis),  Bk.  III.  ch.  iv.  (Ellis 
and  Spedding's  edition,  vol.  iv.  p.  364.) 


350 


FALLACIES  INCIDENT 


the  body  *  in  a  mean  state  '^'  On  this  account,  he 
supposed,  all  animals  which  have  blood  are  furnished 
with  a  brain,  while  bloodless  animals,  having  little  heat, 
require  nothing  to  cool  them,  and  are,  therefore,  with- 
out one.  Moreover,  in  order  to  temper  the  coldness  of 
the  brain,  blood  is  conveyed  to  the  membrane  which 
envelopes  it  by  means  of  veins  or  channels.  But,  agam, 
lest  the  heat  so  conveyed  should  injure  the  brain,  the 
veins,  instead  of  being  large  and  few,  are  small  and 
many,  and  the  blood  conveyed,  instead  of  being  copious 
and  thick,  is  thin  and  pure  ***"'. 

'  The  viscera  are  formed  out  of  the  blood,  and  therefore  are 
only  found  in  sanguineous  animals,  which  necessarily  have  a 
heart  :  for  it  is  clear  that,  having  blood,  which  is  a  fluid,  they 
must  have  a  vessel  to  contain  it,  and  hence  also  Nature  has 
created  veins ;  and  for  these  veins  the  origin  must  necessarily 
be  one,  since  one,  whenever  possible,  is  better  than  many. 
The  heart  is  the  origin  of  the  veins  :  this  is  seen  in  the  fact 
that  they  spring  from  it,  and  do  not  go  through  it ;  also  they 
resemble  it  in  structure.  The  heart  has  the  chief  position, 
namely,  that  of  the  centre,  but  more  upwards  than  down- 
wards, and  rather  in  front  than  behind  :  for  Nature  is  accus- 

»5  Compare  the  extraordinary  fancy  {^De  Partibits  Animalium, 
iii.  4)  that  the  reason  why  the  heart,  in  man,  inclines  slightly  towards 
the  left  side  is  that  it  may  temper  the  greater  coldness  of  that  side 
(TT/jos  TO  dvioovv  rriv  Karaipv^iv  tmv  apiOTtpujv  fmKtara  yap  ruvdWajv 
(,VW  dvepojnos  €X«'  KaT(;vyfitva  rd  dpiarfpa).  It  is  needless  to 
observe  thnt  the  left  side  of  man  is  not  colder  than  the  right ;  the 
fact  is  simply  assumed  in  order  to  account  for  the  position  of  the 
heart  in  a  maimer  conformable  with  Aristotle's  theories. 

^  Dc  Partibus  Animaliiim,  ii.  7.  Cp.  Lewes'  Aristotle,  §  164, 
p.  180. 


TO  INDUCTION 


351 


tomed  to  seat  the  noblest  in  the  noblest  place,  unless  any 
stronger  reason  prevails  :  ou  /xjj  n  kwXvci  [lii^ov  ^^.' 

The  work  of  Bishop  Wilkins,  already  quoted,  furnishes 
some  curious  examples  of  the  arguments  which,  even 
within  the  last  two  hundred  years,  have  found  favour  with 
men  distinguished  for  their  scientific  attainments  ^l 

*  Though  there  are  some  who  think  mountains  to  be  a 
deformity  to  the  earth,  as  if  they  were  either  beat  up  by  the 
flood,  or  else  cast  up  Hke  so  many  heaps  of  rubbish  left  at  the 
Creation  ;  yet,  if  well  considered,  they  will  be  found  as  much 
to  conduce  to  the  beauty  and  conveniency  of  the  universe,  as 
any  of  the  other  parts.  Nature  (saith  Pliny)  purposely  framed 
them  for  many  excellent  uses  :  partly  to  tame  the  violence  of 
greater  rivers,  to  strengthen  certain  joints  within  the  veins 
and  bowels  of  the  earth,  to  break  the  force  of  the  sea's  inun- 
dation, and  for  the  safety  of  the  earth's  inhabitants,  whether 
beasts  or  men  ""■*.' 

*  I  have  now  sufficiently  proved  that  there  are  hills  in  the 
moon,  and  hence  it  may  seem  likely  that  there  is  also  a 
world  ;  for,  since  Providence  hath  some  special  end  in  all  its 
works,  certainly  then  these  mountains  were  not  produced  in 
vain  ;  and  what  more  probable  meaning  can  we  conceive 
there  should  be,  than  to  make  that  place  convenient  for 
habitation  ^  ? ' 

*  It  hath  been  before  confirmed  that  there  was  a  sphere  of 
thick  vaporous  air  encompassing  the  moon,  as  the  first  and 
second  regions  do  this  earth.    I  have  now  showed  that  thence 

*'  De  Partibus  Aninialitan,  iii.  4.  I  here  quote  Mr.  Lewes' 
summary,  given  in  §  395,  p.  310,  of  his  Aristotle. 

^  Bishop  Wilkins  was  one  of  the  founders  of  the  Royal  Society, 
and  enjoyed  one  of  the  highest  scientific  reputations  of  his  time. 

™  A  Discovery  of  a  New  World  in  the  Moon,  p.  77.    ^  Id.  p.  91. 


35^ 


FALLACIES  INCIDENT 


such  exhalations  may  proceed  as  do  produce  the  comets. 
Now  from  hence  it  may  probably  follow  that  there  may  be 
wind  also  and  rain,  with  such  other  meteors  as  are  common 
amongst  us.  This  consequence  is  so  dependent  that  Fro- 
mondus  dares  not  deny  it,  though  he  would  (as  he  confesses 
himself);  for,  if  the  sun  be  able  to  exhale  from  them  such 
fumes  as  may  cause  comets,  why  not  such  as  may  cause 
winds,  why  not  then  such  also  as  may  cause  ram,  since  1 
have  above  showed  that  there  is  sea  and  land,  as  with  us . 
Now  rain  seems  to  be  more  especially  requisite  for  them, 
since  it  may  allay  the  heat  and  scorchings  of  the  sun  when 
he  is  over  their  heads.  And  Nature  hath  thus  provided  for 
those  in  Peru,  with  the  other  inhabitants  under  the  line    . 

One  of  the  most  whimsical  applications  of  the  Argu- 
ment from  Final  Causes  is  to  be  found  in  the  '  Doctrine 
of  Signatures,*  of  which  Dr.  Paris  thus  speaks*^  :— 

*  But  the  most  absurd  and  preposterous  hypothesis  that  has 
disgraced  the  annals  of  medicine,  and  bestowed  medicinal 
reputation  upon  substances  of  no  intrinsic  worth,  is  that  ot 
the  "  DOCTRINE  OF  Signatures,"  as  it  has  been  called, 
which  is  no  less  than  a  belief  that  every  natural  substance, 
which  possesses  any  medicinal  virtues,  indicates,  by  an  ob^ 
vious  and  well-marked  external  character,  the  disease  for 
which  it  is  a  remedy,  or  the  object  for  which  it  should  be 
employed.  This  extraordinary  monster  of  the  fancy  has  been 
principally  adopted  and  cherished  by  Paracelsus,  Baptista 
Porta,  and  Crollius,  although  traces  of  its  existence  may  cer- 
tainly be  discovered  in  very  ancient  authors. 

♦  *♦♦*** 

« The  conceit,  however,  did  not  assume  the  importance  of 

•»  A  Discovery  of  a  New  World  in  the  Moon,  p.  121. 
w  Pharmacologia,  pp.  47-50- 


TO  INDUCTION. 


ZS3 


a  theory  until  the  end  of  the  fourteenth  century,  at  which 
period  we  find  several  authors  engaged  in  the  support  of  its 
truth,  and  it  will  not  be  unamusing  to  ofifer  a  specimen  of 
their  sophistry  :  they  affirm  that,  since  man  is  the  lord  of  the 
creation,  all  other  creatures  are  designed  for  his  use,  and 
therefore  that  their  beneficial  qualities  and  excellences  must 
be  expressed  by  such  characters  as  can  be  seen  and  under- 
stood by  every  one  ;  and  as  man  discovers  his  reason  by 
speech,   and   brutes    their   sensations    by   various    sounds, 
motions,  and  gestures,  so  the  vast  variety  and  diversity  of 
figures,  colours,  and  consistencies,  observable  in  inanimate 
creatures,  is  certainly  designed  for  some  wise  purpose.     It 
must  be,  in  order  to  manifest  those  peculiar  properties  and 
excellences,  which  could  not  be  so  effectually  done  in  any 
other  way,  not  even  by  speech,  since  no  language  is  uni- 
versal.     Thus,  the  lungs  of  a  fox  must  be  a  specific  for 
asthma,  because  that  animal  is   remarkable  for   its   strong 
powers   of  respiration.     Turmerick  has  a  brilliant  yellow 
colour,   which    indicates   that   it   has   the   power   of  curing 
jaundice  ;  by  the  same  rule,  Poppies  must  relieve  diseases  of 
the  head ;  .  . .  and  the  Euphrasia  (eye-bright)  acquired  fame 
as  an  application  in  complaints  of  the  eye,  because  it  exhibits 
a  black  spot  in  its  corolla  resembling  the  pupil.      In  the 
curious  work  of  Chrysostom  Magnenus  (Exercit.  de  Tabaco), 
we  meet  with  a  whimsical  accountof  the  j"/]^;/a///r^  of  tobacco. 
"In  the  first  place,'*  says  he,  "the  manner  in  which  the 
flowers  adhere  to  the  head  of  the  plant  indicates  the  infundi- 
bulum  cerebri,  and  pituitary  gland;  jn  the  next  place,  the 
three  membranes,  of  which  its  leaves  are   composed,   an- 
nounce their  value  to  the  stomach,  which  has  three  mem- 
branes." 

'  The  blood-stone,  the  heliotropium  of  the  ancients,  from 
the  occasional  small  specks  or  points  of  a  blood-red  colour 
exhibited  on  its  green  surface,  is  even  at  this  day  employed 
in  many  parts  of  England  and  Scotland  to  stop  a  bleeding 


354 


FALLACIES  INCIDENT 


from  the  nose ;  the  nettle-tea  continues  a  popular  remedy 
for  ttrticaria. 

<  It  is  also  asserted  that  some  substances  bear  the  SIGNA- 
TURES  of  the  humours,  as  the  petals  of  the  red  rose  that  o 
the  blood,  and  the  roots  of  rhubarb,  and  the   flowers  of 

saffron,  that  of  the  bile.  .        .      .      c      ♦^o^tV. 

*  I  apprehend  that  John  of  Gaddesden,  m  the  fourteenth 
century,  celebrated  by  Chaucer,  must  have  been  directed  by 
some  remote  analogy  of  this  kind,  when  ^-  -^^^'^^^^^l 
of  Edward  I,  who  was  dangerously  ill  with  the  small  pox  to 
be  wrapped  in  scarlet  cloth,  as  well  as  all  those  who  attended 
upon  1 'm,  or  came  into  his  presence ;  and  ev-  the  bed  and 
room  in  which  he  was  laid  were  covered  with  the  same 
drapery;  and  so  completely  did  it  answer,  say  t^^^;''^^"^^"! 
historians  of  that  day,  that  the  prince  was  cured  wUhou. 
having  so  much  as  a  single  mark  left  upon  him. 

In  these  and  similar  instances,  which  might  be  multi- 
plied to  almost  any  extent-  it  is  plain  that  much  is 
gained  by  the  employment  of  the  vague  word  Nature. 
Presuming  that  the  majority  of  at  least  the  more  modern 
writers  who  have  employed  the  Argument  from  Final 
Causes,  if  pressed  to  attach  a  definite  meaning  to  the 
word  Nature,  would  reply  that  they  regard  it,  in  this 
connexion,  as  only  another  name  for  God,  the  argument, 
as  employed  in  the  above  and  similar  examples  (I  am 

^«  The  following  example  (taken  from  Plntarch.  De  Stoicorum 
Kepu,naniiis^  p.  1042,  by  Mr.  Lecky,  in  \^.  History  of  European 
Morals,  from  Augustus  to  Charlemagne,  vol.  n.  p.  I74,  note  2)  1 
perhaps  unsurpassed  in  absurdity:  '  Chrysippus  mamtamed  that 
cock-fighting  was  the  final  cause  of  cocks,  these  buds  bemg  made 
by  Providence  in  order  to  inspire  us  by  the  example  of  their  t:ourage. 


TO  INDUCTION. 


3S5 


not  here  discussing  the  more  refined  employment  of  it), 
seems  to  rest  on  the  three  following  assumptions  : — 

(i)  That  God  [or  Nature]  acts,  not  by  laws,  governing 
the  evolution  of  natural  objects,  but  after  the  manner  of 
a  human  artificer,  having  in  view  some  special  end  in 
the  production  of  each  object  and  of  each  separate  part 
of  it. 

(2)  That  all  objects  are  designed  for  the  good  of  man, 
or,  at  least,  of  .sentient  or  intelligent  beings. 

(3)  That  we  are  so  well  acquainted  with  what  is,  on 
the  whole,  good  for  ourselves,  or  others,  or  the  world 
at  large,  as  wtU  as  with  the  general  plan  of  the  universe, 
that  we  are  able,  in  each  case,  to  pronounce  positively 
on  the  ends  which  God  [or  Nature]  proposed  to  himself 
in  his  constructions  "*. 


•*  The  '  principle '  laid  down  by  Descartes  {De  Principiis  Philo- 
sophic, i.  28)  supplies  an  appropriate  commentary  on  this  assump- 
tion :  *  Ita  denique  nullas  unquam  rationes  circa  res  naturales  a  fine, 
quem  Deus  aut  natura  in  iis  faciendis  sibi  proposuit,  desumemus ; 
quia  non  tantum  nobis  debemus  arrogare,  ut  ejus  consiliorum  parti- 
cipes  nos  esse  putemus.' 

It  is  interesting  to  compare  the  following  extracts  from  Galileo's 
Systema  Cosmiettm,  Dial.  III.    (Sir  Thomas  Salusbury's  translation, 

pp.  33.^,  334)  :— 

*  Salv.  Methinks  we  arrogate  too  much  to  our  selves,  Siniplicius, 

whilst  wc  will  have  it  that  the  onely  care  of  us  is  the  adoequate  work 
and  bound,  beyond  which  the  Divine  Wisdomc  and  Power  doth  or 

disposeth  of  nothing If  one  should  tell  me  that  an  immense 

space  interposed  between  the  Orbs  of  the  Planets  and  the  Starry 
Sphere,  deprived  of  stars  and  idle,  would  be  vain  and  useless,  as 
likewise  that  so  great  an  immensity  for  receipt  of  the  fixed  stars  as 
exceeds  our  utmost  comprehension  would  be  superfluous,  I  would 

A  a  2 


356      FALLACIES  INCIDENT  TO  INDUCTION, 

Of  these  three  assumptions,  the  first  and  second  are, 
as  I  conceive,  based  on  false  analogies,  the  first  trans- 
ferring to  God  [or  Nature]  the  habit,  observed  in  the 
human  artificer,  of  producing  each  object  with  reference 
to  some  special  end,  and  the  second  the  motives  which 
usually  guide  the  artificer  in  the  selection  of  those  ends. 
The  third  assumption,  it  need  hardly  be  added,  involves 
a  generalisation  from  a  very  narrow  range  of  experience 
to  operations  co-extensive  with  all  space  and  all  time. 

Even  though  these  various  errors  have  been  avoided, 
and  the  inductive  process  has  been  correctly  performed, 
it  is  still  possible,  either  through  confusion  of  language, 
through  mistaking  the  question  at  issue,  or  througdi 
drawing  erroneous  inferences  in  our  subsequent  de- 
ductions, to  arrive  at  false  conclusions.  But  these  are 
considerations  which  properly  appertain  to  the  other 
branch  of  Logic,  which  is  concerned  with  deductive 
reasoning. 

reply  that  it  is  rasbnesse  to  go  about  to  make  our  shallow  reason 
judg  of  the  Works  of  God,  and  to  call  vain  and  superfluous  whatso- 
ever  thin^  in  the  Universe  is  not  subservient  to  us.' 

*Sagr!  Say  rather,  and  I  believe  you  would  say  belter,  that  we 
know  not  what  is  subservient  to  us  ;  and  I  hold  it  one  of  the  greatest 
vanities,  yea  follies,  that  can  be  in  the  World,  to  say,  because  I  know 
not  of  what  use  Jupiter  or  Saturn  are  to  me,  that  therefore  these 
Planets  are  superfluous,  yea  more,  that  there  are  no  such  thmgs  in 
rcrum  natural 


INDEX. 


Adnptfition  and  Design,  p.  344. 

Adaequata  causa,  why  the  ex- 
pression is  not  here  em- 
ployed, 121. 

Adequate  hypotheses,  106-112. 

Affirmative  instances,  tendency 
of  the  mind  to  notice,  rather 
than     negative     instances, 

255-259- 
Analogy,  argument    from,   226- 

237- 

—  different    meanings    of    tlie 

word,  226-227. 

—  false,  fallacy  of,  329-356. 
Antiquitas  sa^culi juventus  mundi, 

origin  of  the  apophthegm, 

335- 
Antiquity,  illegitimate  use  of  the 

argument  from,  333-335- 
Aristotle    pointed    out   the   de- 
pendence of  deduction   on 
induction,  241. 

—  his     defective     observation, 

362-263. 

—  his  constant  employment  of 

inductio  per  enumerationem 
simpliccm,  281-283. 

—  his  constant  employment  of 

the     argument    from    final 
causes,  349-35 i* 


Assumptions  made  in  reasoning, 
xi-xvi,  xix-xx. 

Astronomy,  a  science  of  observa- 
tion, 42,  44. 

—  l»eculiarly  rich   in  examples 

of  the  Method  of  Residues, 

175- 

Authority,  illegitimate  use  of  the 

argument  from,  291-298. 
Average  of  observations,  47,  48. 
Averages,    undue    extension    of 

conclusions     based     upon, 

286-289. 

Bacon,  his  condemnation  of  in- 
ductio per  enumerationem 
simplioem,  125,  281. 

—  his  instanti<£  solitaricc^  144, 

M5- 

—  his  instantid!  cruciSy  151 -154. 

—  his  approximation  to  the  in- 

ductive methods,  211-214. 

—  difference   between   his    pro- 

cedure and  that  of  Mr.  Mill, 
in  the  use  of  the  Tables  and 
Methods  respectively,  214. 

—  his  error  with  regard  to  the 

relation  between  the  induc- 
tive and  deductive  pro- 
cesses, 248. 


35^ 


INDEX. 


Bacon,  his  notice  of  the  tendency 
to  take  account  of  affirma- 
tive rather  than  negative 
instances,  255. 

— -  his  criticism  of  the  argument 
from  final  causes,  342-345. 

Bain,  Professor,  referred  to  on 
uniformities  of  co-existence, 
8,  9,  224. 

his  view  of  the  origin  of  uni- 
versal beliefs,  34. 

quoted  with  reference  to  the 

Intermixture  of  Effects,  209. 

Botany,  reasons  for  the  excellence 
of  its  classifications,  55. 

—  nomenclature  of,  89-91. 

—  terminology  of,  92-94. 
Brown,  Dr.  Thomas,  his  view  of 

the  origin  and  nature  of  our 
conception  of  cause,  24-26. 

—  his  objection  to  one  of  Ilume's 

definitions  of  cause,  23. 

Causal  relations,  various  kinds 
of,  126-129. 

Causation,  can  only  be  estab- 
lished by  the  Experimental 
Methods.  7-9,  224,  237. 

Cause,  relation  of,  to  the  con- 
ditions of  a  phenomenon, 
13-16. 

—  nature  of  our  conception  of, 

18-50. 

—  origin  of  our  conception  of, 

25-28. 

—  definition  of,  23-25. 

—  is  an  idea  siii  generis^  23. 

—  error  originating  in  mistaking 


a  joint  cause  for  a  sole  cause, 

305-314- 
Cause,  error  originating  in  mis- 
taking joint  effects  for  cause 
and  effect,  314-3' 8. 

—  error  originating  in  the  con- 

fusion of  the  proximate  with 
the  primary  or  remote  cause 
of  a  phenomenon,  318-322. 

—  error   due    to    neglecting   to 

take  into  account  the  mu- 
tual action  and  reaction 
(mutuality  of  cause  and 
effect,  322-325. 

error  due  to  the  inversion  of 

cause  and  effect,  325-329- 

Causes,  exciting,  15-16. 

—  predisposing,  15-16. 

—  final,  illegitimate  employment 

of  the  argument  from,  342- 

356. 

Certainty,  the  question  whether 
it  be  predicable  of  inductive 
inferences,  ix-xx. 

Characteristick,  84,  85. 

Chemistry,  nomenclature  of,  91. 

—  method  of  difference   exten- 

sively employed  in,  154. 
Classification,  52-89. 

—  scientific,  distinguished  from 

that  employed  in  the  affairs 
of  ordinary  life,  52-55. 

—  scientific,    regarded    as    sub- 

sidiary to  induction,  defini- 
tion of,  54-55- 

—  a  natural  system  of,  distin- 

guished   from    an  artificial 
system  of,  55-57. 


INDEX, 


359 


Classification,  natural,  rules  for 
the  right  conduct  of,  74-80. 

Classifications,  though  subsidiary 
to  inductions,  themselves  de- 
pend on  inductions /^r  cmi- 
mcrationem  simplicetn,  54. 

Co-existence,  Inductions  of,  79, 
54,  223-224. 

Colligation  of  facts,  a  hypothesis 
serves  for,  99-100. 

Comparative  Method,  206. 

Comparison,  Fallacy  of  Exag- 
gerated, 277-278. 

Conditions,  relation  of,  to  the 
cause  of  a  phenomenon,  13- 
16. 

Consent,  Universal,  argument 
from,  297-298. 

Conservation  of  Energy,  Law  of, 
6, 1 29. 

Consilience  of  inductions,  119- 
121. 

Continuity,  law  of,  82-84. 

Crucial  instances,  151-154. 

Darwin,  Mr.,  quoted  on  the  sig- 
nification of  the  word  *  spe- 
cies,' 81-82. 

—  referred  to  on  the  Theory  of 
Final  Causes,  342. 

Deduction,  its  relation  to  induc- 
tion, 241-249;  cp.  xvii  XX. 

Definition,  are  natural  classes 
determined  by  definition  or 
type,  85-89. 

Descartes,his  criticism  of  the  argu- 
ment from  final  causes,  355. 

Diagnosis,  84,  85. 


Empirical  generalisations  or 
laws,  224-226. 

Energy,  Law  of  the  Conserva- 
tion of,  6,  129  ;  cp.  xix. 

Evolution,  course  of,  indicates 
the  existence  and  attributes 
of  the  Supreme  Cause,  342- 

343. 

Exaggerated  comparison,  fallacy 

of,  277-278. 
Exceptio    probat   regulam,   the 

maxim  explained,  309. 
Exceptions  to  rules,   210,  308- 

309- 
Experiment,  39-51. 

—  how    far    employed    by   the 

Greeks,  40. 

—  distinguished    from    observa- 

tion, 39  40. 

—  general    superiority    of,   over 

observation,  40--42. 

—  not  open  to  us  in  the  attempt 

to  ascertain  the  cause  of  a 
given  effect,  42-43. 

—  and     observation,    rules    for 

the  right  conduct  of,  45-51. 
Explanation,    in    the     scientific 
sense,  what,  98-99. 

Fallacies  incident  to  induction, 

254-356. 

—  of  generalisation,  279-356. 

—  common  to  the  employment 

of    the    various     inductive 
methods,  29S-329. 

—  the  same  instance  may  often 

be  indifferently  ascribed  to 
several,  305. 


360 


INDEX. 


Fallacy  of  non-observation,  254- 

1*12. 

arising   from    confusion    be- 
tween absolute  and  relative 
frequency,  259. 
of    non  -  observation    of    in- 
stances, 254-268. 
of  non-observation  of  circum- 
stances attendant  on  a  given 
instance,  268-272. 
_  of  mal-obsersation,  272-278. 

of  exaggerated    comparison, 

277-278.  _ 

—  arising  from  treating  the  m- 
ductio   per   enumerationcm 
simplicem  as  if  it  were    a 
valid  induction,  279-298. 
_  of   *  non    causa    pro   causa,' 

300-7,05. 
-_  due  to  the  neglect  of  a  joint 

cause,  305-314. 
^  due  to  mistaking  joint  effects 
for  cause  and  effect,  314-318. 

due  to  the  confusion  of  the 

proximate  with  the  primary 
or  remote  cause  of  a  phe- 
nomenon, 318-322. 

—  due    to    neglecting    to   take 

into    account    the    mutual 
action    and    reaction    (mu- 
tuality) of  cause  and  effect, 
322-325. 
due  to  the  inversion  of  cause 

and  effect,  325-329- 
.  -  of  false  analogy,  329-.^56- 

—  due  to  the  illegitimnte  employ- 

ment of  argument  from  final 
causes,  342-356. 


Final  causes,  fallacy  due  to  the 
illegitimate  employment  of 
the  argument  from,  342-.^.^6- 

_  legitimate  employment  of  the 
argument  from,  342-344- 

Frequency,  confusion  between 
absolute  and  relative,  259. 

Frequency  of  occurrence  docs  not 
always  furnish  an  argument 
for    the    recurrence    of    an 
event,  288-2S9. 
Frustration  of  Effects,  307-309- 

Galileo,  quoted  on  the  theor\'  of 
Final  Causes,  355-356- 

Geology  aboimds  in  instances 
of  the  employment  of  the 
method  of  concomitant  vari- 
ations, 193. 

God  ;  see  Supreme  Cause. 

Nature  often  used  indefinitely 

for,  354-356. 

Hamilton.  Sir  W.,  his  criticism 
of  Hume's  theory  on  the 
nnture  of  cause,  22. 

Ilerschel,  Sir  John,  distinctly 
recognises  the  inductive 
methods,  210. 

quoted   on   our   tendency   to 

notice     affirmative      rather 
than      negative      instances, 

256-257- 
IIi^torical     Method,     204-207, 

252. 
Hume,  liis  view  of  the  nature  of 
our  conception  of  cause,  18- 

I  30- 


INDEX. 


361 


Hume,  injustice  done  to  him  by 
quoting  from  his  treatise  of 
Human  Nature,  29-30. 

Hypothesis,  xviii-xix,  Ii-13» 
97-123,  248-249. 

—  always    suggested     by    facts 

within  our  experience,  xviii, 
248. 

—  distinction   between,  and   in- 

duction, I1-13,  1 12-115. 

—  description  of,  97-99. 

—  conditions    of    a    legitimate, 

100-I13. 

—  difference  between   Mr.  Mill 

and  Dr.  Whewell  as  to  the 
functions  of,  115-121. 

—  views  of  Professor  Jcvons  on 

the   relation    of  hypothesis 
to  induction,  xvi  -xix,  1 1 7. 

—  gratuitous,  122-123. 
Hypothetical,  all  reasoning  is  in 

a  sense,  xi-xvi ;  cp.  xix. 

Imaginative  Faculty,  Formation 
of  Hypotheses  the  work  of, 
100. 

Inductio  per  enumerationcm  sim- 
plicem, 7-9,  124-126,  219- 
226. 

—  complete,  125,  219. 

—  distinction  between  complete 

and  incomplete,  219-220. 

—  distinguished  from  the  Method 

of  Agreement,  222,  226. 

—  fallacy     arising,     in     certain 

cases,  from  its  employment 
as  if  it  were  a  scientific  in- 
duction, 2S0-298. 


Inductio  per  enumerationcm  sim- 
plicem, its  employment  by 
Aristotle,  281-283. 

—  instance   of  its   employment 

in   the    Science    of  Proba- 
bility, 286-288. 

—  is  still   commonly  employed 

in  social  speculations,  289- 
291. 
Induction,  ambiguous  use  of  the 
word,  3. 

—  the  nature  of,  3-10,  124-126; 

cp.  xviii,  xix. 

—  defined,  9-10. 

—  does   it  admit   of   certainty, 

ix-xx. 

—  distinction  between,  and  hy- 

pothesis, 11-13- 

—  question  whether  it  be  from 

the  particular  to  the  general, 
or  from  particulars  to  ad- 
jacent particulars,  16-18. 

—  its  relation  to  deduction,  241- 

249;  cp.  xvii-xx. 

—  fallacies  incident  to,  254-356. 
Inductions  of  Co-existence,  7-9, 

54,  223-224. 

—  of  Causation,  8-9,  125   126, 

224. 

—  of  Equality,  8-6. 

—  imperfect,  219-240. 

—  incomplete,  237-240. 
Inductive     Methods,     124-218, 

222-223. 

—  their  object,    126,  216,  222- 

223,  299. 

—  reducible  to  two  only,  207-208. 

—  distinctly  recognised    by   Sir 


362 


INDEX, 


John  Herschel,  tliough  the 
importance  now  attached  to 
them  is  mainly  due  to  Mr. 
Mill,  2IO. 
Inductive  Methods,  approxima- 
tions to,  in  the  Novum  Or- 
ganiun,  210-214. 

—  defended  against  the  attacks 

of  Dr.  Whewell,  214-218. 

—  imperfect  applications  of,2  37- 

24c. 

—  fallacies  common  to  the  em- 

ployment   of    the    various, 

398-329. 
Intentional  Species,  123. 
Intermixture  of  effects,  208-210. 
Invariable  conjunction,  130,  137- 

138,  I4.=^-I47»  163-164,170; 

cp.  48-49»  134- 
Inverse  Deductive  Method,  205, 

252. 
Isolation    of    phenomena,     im- 
portance of,  50-51. 

Jevons,  Professor,  referred  to  on 
the  question  whether  induc- 
tion be  from  the  particular 
to  the  general,  or  from  par- 
ticulars to  adjacent  par- 
ticulars, 17. 

—  on    rules    for   legitimate  hy- 

potheses, lOI. 

—  on  the  relation  of  Hypothesis 

to  Induction,  xvi  xix. 

—  on  ihe  uncertainty  attaching 

to  inductive  inference, ix-xx. 

—  on  the  nature  of  inductive  in- 

ference, ix-xx,  117. 


Kant,  his  criticism  of  Hume's 
account  of  causation,  26-27. 

Law  of  uniformity  of  nature,  5- 

9>  30-38- 
—  of  universal  causation,   4-9, 

30-38- 

Laws  of  Thought,  xix-xx. 

Lewes,  Mr.,  criticism  of  his 
statements  on  the  belief  in 
the  law  of  universal  causa- 
tion, 30-32. 

Locke,  his  account  of  the  idea  of 
power,  19-20. 

Maine  de  Biran,  M.,  his  view  of 
the  nature  of  our  conception 
of  cause,  27. 

Malebranche,  his  idea  of  causa- 
tion, 18. 

Mansel,  Dr.,  his  view  of  the  na- 
ture of  our  conception  of 
cause,  27-28. 

—  his  view  of  the  origin  of  our 

beliefs  in  the  laws  of  uni- 
versal causation  and  the 
uniformity  of  nature,  .-,6. 

Material  and  immaterial  circum- 
stances, 48-49, 134-' 35- 

Medicine, » distinction  of  exciting 
and  predisposing  causes  in, 
15-16. 

Method  of  Agreement,  130-148. 

—  of  difference,  H'^-iSQ- 

—  double,  of  agreement  (or  joint 

method   of  agreement   and 
difference),  160-173. 

—  of  residues,  173-182. 


INDEX. 


Z^?^ 


Method  of  concomitant  varia- 
tions, 183-206. 

—  of  concomitant  variations,  Mr. 

Bain  quoted  on  its  applica- 
tion in  the  case  of  Inter- 
mixture of  Effects,  205-209. 

—  comparative,  206. 

—  historical,  204-207,  252. 

Method  of  Agreement  distin- 
guished from  Inductio  per 
Enumerationem  Simpliccm, 
222,  226. 

Methods,  inductive  or  experi- 
mental, 124-218,  222-223. 

Mill,  James,  quoted  on  the  origin 
of  our  belief  in  the  law  of 
universal  causation,  34-35. 

Mill,  J.  S.,  referred  to  on  the  re- 
lation between  the  cause  and 
the  conditions  of  a  pheno- 
menon, 14-15- 

—  question  between  him  and  Dr. 

Whewell,  as  to  whether  in- 
ductive inference  be  from 
the  particular  to  the  general, 
or  from  particulars  to  adja- 
cent particulars,  16-18. 

—  his  definition  of  cause  criti- 

cised, 24. 

—  his  answer  to  Reid's  objection 

to  Hume's  account  of  causa- 
tion, 24-25. 

—  his  view  of  the  origin  of  uni- 

versal beliefs,  34-36. 

—  difference  between  him  atid  Dr. 

Whewell  as  to  the  function 
of  hypotheses,  11 5-1 21. 

—  importance  now  attached  to 


the  inductive  methods  main- 
ly due  to  his  influence,  210. 

Mill,  J.  S.,  on  the  Law  of  Iden- 
tity, XX. 

Mineralogy,  mainly  a  classifica- 
tory  science,  55. 

Natural  distinguished  from  arti- 
ficial classification,  55-57* 

—  classification,    rules   for    the 

right  conduct  of,  74-80. 

—  groups,  arrangement  of,  in  a 

natural  series,  77-80. 

—  groups,  constant   recognition 

of  new,  82-84. 

—  Selection,  its  relation  to  doc- 

trine of  Pinal  Causes,  342- 

343. 

Nature,  substituted  by  Aristotle 

for  God,  349-351- 

—  vague   employment    of   the 

term,  354-356 ;  cp.  342-  343- 
Newton,  his  demonstration  of  a 
central  foice,  11 3- 115. 

—  his    employment   of  the   ex- 

pression *  Vera  Causa,'  121- 

122. 
Nomenclature,  89-91. 
Non  causa  pro  causa,  305. 

Observation,  39-51. 

— distinguished  from  experiment, 

39-40. 

—  general  employment  of,  pre- 

ceded that  of  experiment,40. 

—  alone  open   to  us  in  the  at- 

tempt to  ascertain  the  cause 
of  a  given  effect,  42-43. 


3^4 


INDEX. 


Observation,  sciences  wholly  or 
mainly  dependent  on,  at  a 
great  disadvantage,  as  com- 
pared with  those  in  which 
we  can  largely  employ  ex- 
periment, 43-45- 

—  and  experiment,  rules  for  the 
right  conduct  of,  45~"5^* 

Observations,  importance  of 
taking  an  average  of,  47-48* 

Ogle,  Dr.  William,  his  Intro- 
duction to  the  De  Partibus 
Animaliiim  referred  to,  282. 

Physiology  frequently  employs 
the  method  of  concomitant 
variations,  195-19^' 

Plato,  his  employment  of  the 
argument  from  final  causes, 

345-349- 
Plurality  of  causes,  6,  23,  127- 

128,  131-134- 

—  fallacy  arising  from  neglect- 
ing to  take  into  account,  305. 

Post  hoc,  ergo  propter  hoc,  305. 

Power,  question  whether  the 
idea  of  is  involved  in  our 
conception  of  cause,  18-30. 

Prediction,  value  to  be  attached 
to,  117-121. 

Read,  Mr.  Carvcth,  his  expres- 
sion *  Vicariousness  of 
Causes,'  127. 

Reid,  his  criticism  of  Hume's  ac- 
count of  causation,  21-25. 

—  his  view  of  the  nature  of  our 
conception  of  cause^  27. 


Reid,  his  view  of  ths  origin  of 
universal  beliefs,  32  -33. 


Social  questions,  the  extreme  dif- 
ficulty attendant  on  their  in- 
vestigation, 289-291. 

Species,  practice  of  naturalists  in 
stopping  at,  open  to  ques- 
tion, 80-82. 

—  and  varieties,  constant  recog- 

nition of  new,  82-84. 
Spencer,  Herbert,  his  view  of  the 
origin  of  universal    beliefs, 

36-37- 

—  referred  to  on  the  Theory  of 

Final  Causes,  342. 
Statistics,  conclusions  based  on, 
are  instances  of  the  appli- 
cation   of   the    method    of 
concomitant  variations,  204. 
Stewart,  Dugald,  his  view  of  the 
nature  of  our  conception  of 
cause,  27. 
Subordination  of  characters,  prin- 
ciple of,  74-75- 
Supreme   Cause,  the    course  of 
evolution  an   indication    of 
His  existence  and  attributes, 

342-343- 


Terminology,  92-97. 

Theory,  two  meanings  of  the 
word,  13. 

Thermotics,  Science  of,  furnishes 
good  examples  of  the  Me- 
thod of  Difference,  155. 

Type,  persistency  of,  83-84. 


INDEX. 


365 


\ 


Type,  are  natural  classes  deter- 
mined by  definition  or,  85- 
89. 

Ultimate  laws  of  nature,  225. 
Uniformity   of   nature,   law   of, 

5-9- 

—  converse  does  not  hold  true,  6. 

—  vaguer  and  more  precise  mean- 

ings of  the  expression,  9. 

—  universality  of  the  belief  in, 

30-32  ;  cp.  xi-xvi. 

—  origin   of  the  belief  in,  7-9, 

30-38- 
Universal  beliefs,  various  theo- 
ries as  to  the  origin  of,  30- 

38. 
Universal  causaUon,law  of,  4-9. 

—  universality  of  the  belief  in, 

30-32  ;  cp.  xv-xvi. 

—  origin  of  the  belief  in,  30-38. 

Variation  of  circumstances,  im- 
portance of,  49. 

Venn,  Mr.,  referred  to  on  a  com- 
mon fallacy  in  the  calcula- 
tion of  probabilities,  286- 
288. 

Vera  causa,  why  the  expression 


is  not  here  employed,  121- 

122. 
Verification,  249-253. 
Veritas  temporis  filia  dicitur,  non 

auctoritatis,    origin    of  the 

apophthegm,  334-335* 

Whewell,  Dr.,  que?tion  between 
him  and  Mr.  Mill  as  to  whe- 
ther inductive  inference  btf 
from  the  particular  to  the 
general,  or  from  particulars 
to  adjacent  particulars,  16- 
18. 

—  his    view    of  the    origin    of 

universal  beliefs,  33. 

—  his      position     that     natural 

classes  are  determined  not 
by  definition  but  by  type, 
85-89. 

—  his  remarks  on  terminology, 

93-96. 

—  difference   between   him  and 

Mr.  Mill  as  to  the  function 
of  hypotheses,  11 5-1 21. 

—  his  criticism  on  the  inductive 

methods,  214-218. 

Zoology,  reasons  for  the  excel- 
lence of  itsclassifications,55. 


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